Power Play Class 8 Worksheet with Answers Maths Chapter 2 - #NCSOLVE 📚

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Class 8 Maths Chapter 2 Power Play Worksheet with Answers Pdf

Power Play Class 8 Maths Worksheet

Class 8 Maths Chapter 2 Worksheet with Answers – Class 8 Power Play Worksheet

Multiple Choice Questions.

Question 1.
What is the value of 5^-3 ?
(a) \(\frac{1}{5^3}\)
(b) -5³
(c) –\(\frac{1}{5^3}\)
(d) -5³
Answer:
(a) \(\frac{1}{5^3}\)

Question 2.
If a – 2 and b = – 3 then what is ab ?
(a) 8
(b) \(\frac{1}{8}\)
(c) -8
(d) \(\frac{1}{4}\)
Answer:
(b) \(\frac{1}{8}\)

Question 3.
Which of the following is equal to \(\left(\frac{3}{4}\right)^{-2}\)
(a) \(\left(\frac{4}{3}\right)^2\)
(b) \(\left(\frac{3}{4}\right)^2\)
(c) \(\frac{3}{4}\)
(d) \(\frac{4}{3}\)
Answer:
(a) \(\left(\frac{4}{3}\right)^2\)

Question 4.
Simplify (2^-3.2⁴).
(a) 2⁷
(b) (2)^-7
(c) 2
(d) \(\frac{1}{2}\)
Answer:
(c) 2

Question 5.
What is the value of (3^-2)^-1?
(a) 32
(b) \(\frac{1}{3^2}\)
(c) 3^-2
(d) 9^-1
Answer:
(a) 32

Question 6.
If a lock uses 4 slots with digit 0-5 then the possible combinations are
(a) 4⁵
(b) 5⁴
(c) 6⁴
(d) 4⁶
Answer:
(c) 6⁴

Question 7.
Simplify (2³ x 2⁵) ÷ 2⁴
(a) 2⁴
(b) 2³
(c) 2²
(d) 2
Answer:
(a) 2⁴

Question 8.
If 5^a ÷ 5² = 5⁷ then the value of a is
(a) 2
(b) 5
(c) -5
(d) 9
Answer:
(d) 9

Question 9.
If a bacterial population doubles every day and initially there are 1000, then after 3 days the number of bacteria will be
(a) 4000
(b) 2000
(c) 8000
(d) 6000
Answer:
(c) 8000

Question 10.
A car runs 50 km on day 1, 60 km on day 2, 70 km on day 3 and so on . This is
(a) linear growth
(b) exponential growth
(c) random growth
(d) No growth
Answer:
(a) linear growth

Question 11.
If the cost of a land increases linearly at ₹ 5000 per year. If initial cost of the land is ₹ 50000 then the value after 6 years is
(a) ₹ 70000
(b) ₹ 80000
(c) ₹ 60000
(d) ₹ 125000
Answer:
(b) ₹ 80000

Question 12.
The Thickness of a paper sheet is becomes
(a) 0.4096 cm
(b) 4.096 cm
(c) 40.96 cm
(d) 409.6 cm
Answer:
(b) 4.096 cm

Question 13.
Which of the following represents
(a) 2⁴ × 3⁴ × 5²
(b) 2⁴ × 3² × 5²
(c) 2² × 3⁴ × 5²
(d) 2² × 3² × 5³
Answer:
(a) 2⁴ × 3⁴ × 5²

Question 14.
Simplify (10⁴ ÷ 5⁴)
(a) 2
(b) 50⁴
(c) 2⁴
(d) 20⁴
Answer:
(c) 2⁴

Question 15.
If 9^2x-3 = 729 then the value of x is
(a) 2
(b) 3
(c) 4
(d) 6
Answer:
(b) 3

Question 16.
Which of the following is the standard form of 0.00001275?
(a) 1.275 × 10⁵
(b) 1.275 × 10^-5
(c) 127.5 × 10^-7
(d) 127.10⁷
Answer:
(b) 1.275 × 10^-5

Question 17.
Which of the following is the standard form of \(\frac{3456}{1000000}\)?
(a) 0.0003456
(b) 0.0000003456
(c) 3.456 × 10^-2
(d) 3.456 × 10^-3
Answer:
(d) 3.456 × 10^-3

Question 18.
Which of the following is larger?
(a) 2.3 × 10²
(b) 23.2 × 10
(c) 232 × 10^-1
(d) 232000 × 10^-2
Answer:
(d) 232000 × 10^-2

Question 19.
Convert 0.00004 56 to standard form. Which of the following is true regarding the exponent in the standard form ?
(a) The exponent is -4
(b) The exponent is -5
(c) The exponent is -6
(d) The exponent is -7
Answer:
(b) The exponent is -5

Question 20.
If x = 2.5 × 10^-3 andy = 1.5 × 10^-4 ‘then which of the following is true about x + y when expressed in standard form?
(a) 4.0 × 10^-3
(b) 1.75 × 10^-4
(c) 2.65 × 10^-4
(d) 0.00265
Answer:
(d) 0.00265

Question 21.
Which one of the following is equal to \(\left(\frac{100}{9}\right)^{\frac{-3}{2}}\)?
(a) \(\left(\frac{9}{100}\right)^{\frac{-3}{2}}\)
(b) \(\frac{1}{\left(\frac{100}{9}\right)^{\frac{2}{3}}}\)
(c) \(\frac{3}{10} \times \frac{3}{10} \times \frac{3}{10}\)
(d) \(\sqrt{\frac{100 \times 100 \times 100}{9 \times 9 \times 9}}\)
Answer:
(c) \(\frac{3}{10} \times \frac{3}{10} \times \frac{3}{10}\)

Question 22.
For a non-zero rational number z, (z^-2)³ is equal to
(a) z⁶
(b) z^-6
(c) z¹
(d) z⁴
Answer:
(b) z^-6

Question 23.
The exponential form of 456 is
(a) 2² × 19
(b) 2² × 3² × 19
(c) 2³ × 3 × 19
(d) 3³ × 19
Answer:
(c) 2³ × 3 × 19

Question 24.
(1)^-58 is equal to
(a) 1
(b) -1
(c) 1⁵⁸
(d) 0
Answer:
(a) 1

Question 25.
The standard form for 234000000 is
(a) 2.34 × 10⁸
(b) 0.234 × 10⁹
(c) 2.34 × 10^-8
(d) 0.234 × 10²
Answer:
(a) 2.34 × 10⁸

Question 26.
Which of the following is correct?
(a) n^a × n^b = n^ab
(b) (n^a)^b = n^a+b
(c) n^a + n^b = n^a-b
(d) n⁰ = 0
Answer:
(c) n^a + n^b = n^a-b

Question 27.
Which grows faster?
(a) Linear growth
(b) Exponential growth
(c) Both (a) and (b)
(d) Can not compared
Answer:
(b) Exponential growth

Question 28.
If a lock has 5 slot with digit 0-9 then the number of possible codes is
(a) 1000
(b) 105
(c) 510
(d) 50
Answer:
(b) 105

Question 29.
Simplify 2⁵ × 5⁵
(a) 50²⁵
(b) 10²⁵
(c) 10⁵
(d) 50⁵
Answer:
(c) 10⁵

Question 30.
If production capacity of a company doubles every 2 years and the initial production quantity in 2025 was 5000 units. What will be the company’s production quantity after 6 years?
(a) 20,000
(b) 40,000
(c) 30,000
(d) 30,000
Answer:
(b) 40,000

Question 31.
The scientific notation of 0.00000000052 is
(a) 5.2 × 10^-30
(b) 5.2 × 10^-9
(c) 52 × 10^-11
(d) 0.52 × 10⁹
Answer:
(a) 5.2 × 10^-30

Question 32.
If each tree has 10000 leaves and total trees are 32000 then the total number of leaves in standard form is
(a) 3.2 × 10⁸
(b) 3.2 × 10⁷
(c) 0.32 × 10⁷
(d) 32 × 10⁸
Answer:
(a) 3.2 × 10⁸

Question 33.
The distance between Sun and Earth is 1.496 × 10¹¹ m. This is the standard form of
(a) 14,56,00,000 m
(b) 1,49,60,00,000 m
(c) 14,96,00,00,000 m
(d) 1,49,60,00,00,000 m
Answer:
(d) 1,49,60,00,00,000 m

Question 34.
The scientific notation of (0.00084 × 3.2 × 10⁵) + (4.2 × 10²) is
(a) 6.4 × 10²
(b) 0.64 × 10⁴
(c) 6.4 × 10³
(d) 64 × 10³
Answer:
(c) 6.4 × 10³

Assertion Reason Type Questions.

1. Assertion (A) 1.5 × 10⁴ is a way to express a small number in standard form.
Reason (R) Numbers less than 1 can be written using negative exponents to indicate the number of decimal places.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertici.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.
Answer:
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion

2. Assertion (A) 6.3 × 10² is equal to 0.063.
Reason (R) When converting to standard form, the negative exponent indicabs the number of places to move the decimal point to the right.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.
Answer:
(c) Assertion is true but Reason is false.

3. Assertion (A) 0.00034 can be written as 3.4 × 10⁴.
Reason (R) In scientific notation, we move the decimal point until one non-zero digit remains on the left.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation cf Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.
Answer:
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

4. Assertion (A) 7.2 × 10³ is the standard form or scientific notation of 7200.
Reason (R) When converting to standard form, if we move the decimal in left direction the exponent value will be positive. .
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.
Answer:
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

Fill in the blanks.

1. 2^-6 is equal to ___________.
Answer:
\(\frac {1}{64}\)

2. In 10^-30, exponent is ___________ and base is ___________.
Answer:
-30, 10

3. If 16 = 2 × 2 × 2 × 2 = 2⁴ then \(\frac{1}{16}\) can be expressed as 2 raised to the power ___________.
Answer:
-4

4. If 27 = 3 × 3 × 3 = 3³ then (27)^-2 can be expressed as a power with the base 3 by ___________.
Answer:
-6

5. The exponential form of 1728 is ___________.
Answer:
2⁶ × 3³

6. (12)° is equal to ___________.
Answer:
1

7. The standard form of 0.00056 is 5.6 × 10^-x then the value of x = ___________.
Answer:
4

8. 3.4 × 10⁴ is written as ___________.
Answer:
0.00034

9. The number 7.2 × 10² is equal to ___________.
Answer:
0.072

10. 2.5 × 10³ in decimal form is ___________.
Answer:
0.0025

11. The standard form of 0.000072 is ___________.
Answer:
7.2 × 10^-5

State whether the statements given below are true or false.

1. (3^-2) = \(\frac {1}{9}\)
Answer:
True

2. (x^a. x^b = x^a-b) is true for any integers a and b.
Answer:
False

3. \(\left(\frac{2}{3}\right)^{-3}=\frac{3^3}{2^3}\)
Answer:
True

4. The exponent rule (a^m)ⁿ – a^mn also holds for negative values of m and n.
Answer:
True

5. 2^-4 = \(\frac {1}{16}\)
Answer:
True

6. Very small numbers can be expressed in standard form using negative exponents.
Answer:
True

7. The standard form of 0.08 is 8 × 10².
Answer:
True

8. 2.8009 × 10⁹ into its usual form is 28009000000.
Answer:
False

9. The standard form of 0.0000000123 is 1.23 × 10^-8.
Answer:
True

10. The sum of 2.64 × 10²⁴ kg and 4.0035 × 10³⁰ kg is 4.00350264 × 10³⁰ kg.
Answer:
True

11. The difference between 0.0000265 m and 0.00000365 m is 2.285 × 10⁵ m.
Answer:
True

Match the following.

Question 1.

Column I	Column II
(i) aman	(a) 1
(ii) \(\left(\frac{a}{b}\right)^{-n}\)	(b) \(\left(\frac{a^{-n}}{b^{-n}}\right)\)
(iii) a-n	(c) amn
(iv) a0	(d) \(\frac{1}{a^n}\)
(v) (am)n	(e) am+n

Answer:

Column I	Column II
(i) aman	(e) am+n
(ii) \(\left(\frac{a}{b}\right)^{-n}\)	(b) \(\left(\frac{a^{-n}}{b^{-n}}\right)\)
(iii) a-n	(d) \(\frac{1}{a^n}\)
(iv) a0	(b) \(\left(\frac{a^{-n}}{b^{-n}}\right)\)
(v) (am)n	(c) amn

Question 2.

Column I	Column II
(i) 12 × 101	(a) 1200
(ii) 12 × 10-4	(b) 0.000012
(iii) 1.2 × 10-5	(c) 0.00012
(iv) 12 × 10-6	(d) 0.0000012
(v) 12 × 103	(e) 12

Answer:

Column I	Column II
(i) 12 × 101	(e) 12
(ii) 12 × 10-4	(c) 0.00012
(iii) 1.2 × 10-5	(b) 0.000012
(iv) 12 × 10-6	(d) 0.0000012
(v) 12 × 103	(a) 1200

Question 3.

Column I	Column II
(i) 0.045	(a) 0.0000213
(ii) 7000000	(b) 5.6 × 103
(iii) 5600	(c) 7 x 106
(iv) 2.13 × 105	(d) 4.5 × 10 2
(v) 8.9 × 103	(e) 8900

Answer:

Column I	Column II
(i) 0.045	(d) 4.5 × 10 2
(ii) 7000000	(c) 7 x 106
(iii) 5600	(b) 5.6 × 103
(iv) 2.13 × 105	(a) 0.0000213
(v) 8.9 × 103	(e) 8900

Complete the table. One has been done for you.

Question 1.

Expression	Simplified Form
(i) 7-2	(a) _______________
(ii) _______________	(b) 4500
(iii) 10°	(c) _______________
(iv) (3-1)2	(d) _______________
(v) a-3 .a2	(e) _______________
(vi) _______________	(f) 400
(vii) (52. 5-5)	(g) _______________

Answer:

Expression	Simplified Form
(i) 7-2	(a) \(\frac{1}{49}\)
(ii) 22 × 32 × 53	(b) 4500
(iii) 10°	(c) 1
(iv) (3-1)2	(d) \(\frac{1}{9}\)
(v) a-3 .a2	(e) \(\frac{1}{a}\)
(vi) 42 × 52	(f) 400
(vii) (52. 5-5)	(g) \(\frac{1}{125}\)

Question 2.

Small Number/Larger Number	Standard Form
(i) 0.000000345	3.45 × 10-7
(ii) 78699900000000000000
(iii) 0.0000000000000000000000000000045
(iv) 0.76890000000000
(v) 200000000000000
(vi) 140000000000
(vii) 0.000000000000000123
(viii) 123000000

Answer:

Small Number/Larger Number	Standard Form
(i) 0.000000345	3.45 × 10-7
(ii) 78699900000000000000	7.86999 × 1019
(iii) 0.0000000000000000000000000000045	4.5 × 10
(iv) 0.76890000000000	7.689 × 10-1
(v) 200000000000000	2 × 1014
(vi) 140000000000	1.4 × 1011
(vii) 0.000000000000000123	1.23 × 10-16
(viii) 123000000	123 × 108

Very Short Answer Type Questions.

(i) In a stack, there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?
Answer:
1.0008 × 10² mm

(ii) If \(\frac{p}{q}=\left(\frac{3}{2}\right)^{-2} \div\left(\frac{6}{7}\right)^0\) then find the value of \(\left(\frac{p}{q}\right)^{-3}\).
Answer:

(iii) Express 5 × 5 × 6 × 6 × 7 × 7 in the exponential form. .
Answer:
5² × 6² × 7²

(iv) Simplify the expression 11² × 11^-5 × 11⁶.
Answer:
(11)³

(v) The volume of the Earth is approximately 7.67 × 10^-7 times the volume of the sun. Express this number in usual form.
Answer:
0.000000767

(vi) Expand the number 54321 in power of 10.
Answer:
5 × 10⁴ + 4 × 10³ + 3 × 10² + 2 × 10 + 1 × 10⁰

Short Answer Type Questions.

(i) The cells of a bacteria double itself every hour. How many cells will there be after 8 hrs, if initially we start with 1 cell? Express the answer in power.
Answer:
2⁸

(ii) Assuming that x is a positive real numbers and a, b and c are rational numbers.
Show that \(\left(\frac{\chi^a}{\chi^b}\right)^{(a+b-c)} \times\left(\frac{\chi^b}{\chi^c}\right)^{(b+c-a)} \times\left(\frac{\chi^c}{\chi^a}\right)^{(c+a-b)}\) = 1
Answer:

(iii) A shelf is having total thickness of the books as 2.48 × 10² mm. If 6 books each of thickness 25 mm are taken out of the 20 books. Then, find the thickness of each of the remaining books which are equal in thickness.
Answer:
7 mm

(iv) A new born bear weights 4 kg. How many kilograms might a five year old bear weight, if its weight increases by the power of 2 in 5 years?
Answer:
16 kg

(v) Rohan has 5 dresses, 2 hats and 3 pairs of shoes. How many different ways can Rohan dress up?
Answer:
30

(vi) A particular star is at a distance of about 8.1 × 10¹³ km from the earth. Assuming that the light travels at 3 × 10⁸ m per sec, find how long does light take from that star to reach the earth.
Answer:
2.7 × 10⁸ seconds

Long Answer Type Questions

(i) Simplify each expression to its simplest form.
(a) (2³ × 5^-2)²
(b) \(\frac{3^{-4} \times 9^2}{(27)^{-1}}\)
(c) (10⁴ ÷10^-3)²
Answer:
(a) \(\frac{64}{625}\)
(b) 27
(c) 10¹⁴

(ii) Express the given information in standard form and then arrange them in ascending order of their size.

Deserts of the world	Area (sq. km)
Kalahari, South Africa	932400
Thar, India	199430
Gibson, Australia	155400
Great Victoria, Australia	647500
Sahara, North Africa	8598800

Answer:
(a) 9.324 × 10⁵
(b) 1.9943 × 10⁵
(c) 1.554 × 10⁵
(d) 6.475 × 10⁵
(e) 8.5988 × 10⁶

Gibson < Thar < Great Victoria < Kalahari < Sahara

(iii) A company manufactures tiny microchips with dimensions 5 × 10³ m in length, 2 × 10^-3 m in width and 1 × 10³ m in height
(a) Calculate the volume of one microchip using the formula, volume = length × width × height. Express your answer in cubic metres using exponents.
(b) If the company produces 106 microchips then what would be the total volume of all the microchips produced? Express the total volume in standard form.
Answer:
(a) 1 × 10^-8 cubic metres
(b) 1 × 10^-2 cubic metres

Case based question.

In a Science class, the teacher discussed the distances between various celestial bodies in our solar system. The students were provided with the following information to answer the questions.

• Distance from Earth to the Moon: 3.84 × 10⁵ km.
• Distance from Earth to Mars: 7.8 × 10⁷ km.
• Distance from Earth to Jupiter: 6.28 × 10⁸ km.

On the basis of the above information, answer the following questions.
(i) What is the distance from Earth to the Moon in scientific notation (in metres)?
(ii) What is the approximate distance from Earth to Mars in scientific notation (in metres)?
(iii) How many times is the distance from Earth to Jupiter greater than the distance from Earth to the moon?
(iv) If a space probe takes 2 × 10³ seconds to travel from Earth to the Moon, calculate its speed in metres per second using the distance provided in scientific notation. Show your calculations step by step and explain the rules of exponents you applied to simplify the expression.
(Note speed = distance/time)
Answer:
(i) 3.84 × 10⁸ m
(ii) 7.8 × 10¹⁰ m
(iii) 1.635 × 10³
(iv) 1.92 × 10⁵ m/s

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