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Power Play: questions with answers

Class 8 Maths, Chapter 2 (NCERT). 15 questions by concept. Open “Show answer” for the answer and why.

How to teach this chapter · Common misconceptions & worked visual for this chapter

Exponential growth is multiplicative; linear growth is additive

Question 1

The lotuses in a pond double every day, and the pond is completely covered on day 36. How much of the pond was covered on day 18?

  1. (a)A quarter of the pond
  2. (b)118\frac{1}{18} of the pond
  3. (c)1218\frac{1}{2^{18}} of the pond
  4. (d)Half of the pond
Show answer

(c) 1218\frac{1}{2^{18}} of the pond

There are 18 doublings from day 18 to day 36. Divide the full coverage by 2 to power 18, giving 1218\frac{1}{2^{18}} of the pond.

Question 2

A dish holds 5 bacteria, and the number doubles every hour. How many are there after 4 hours?

  1. (a)20
  2. (b)40
  3. (c)80
  4. (d)25
Show answer

(c) 80

Multiply the initial 5 by 2 once per hour. After 4 hours the count is 80.

Writing a number as a product of powers of its prime factors

Question 3

What is 7×337 \times 3^{3}?

  1. (a)9261
  2. (b)63
  3. (c)27
  4. (d)189
Show answer

(d) 189

Evaluate the power first: 3 to power 3 is 27. Then multiply by the coefficient 7, giving 189.

Question 4

A number is written as 43×924^{3} \times 9^{2}. In its PRIME factorisation, how many times does 2 appear?

  1. (a)3
  2. (b)10
  3. (c)6
  4. (d)2
Show answer

(c) 6

Each 4 contains two factors of 2. Repeating it 3 times gives 6 factors of 2.

(n^a)^b = n^(a x b), and the several ways to split one power

Question 5

Aarav writes 262^{6} = (22)3(2^{2})^{3}. Bhavna writes 262^{6} = (23)3(2^{3})^{3}. Who is right?

  1. (a)Both are right.
  2. (b)Only Aarav is right.
  3. (c)Neither -- it should be 252^{5}.
  4. (d)Only Bhavna is right.
Show answer

(b) Only Aarav is right.

For a power of a power, multiply the exponents. Aarav gives exponent 6, but Bhavna gives 9.

Question 6

Which of these is equal to (73)2(7^{3})^{2}?

  1. (a)737^{3}
  2. (b)757^{5}
  3. (c)2×732 \times 7^{3}
  4. (d)767^{6}
Show answer

(d) 767^{6}

There are 2 groups of 3 factors. Multiply the exponents to obtain 6, giving 767^{6}.

What n raised to the power a means, and what its sign is

Question 7

What is (−3)2(-3)^{2}?

  1. (a)-9
  2. (b)-6
  3. (c)9
Show answer

(c) 9

There are 2 negative factors. Since 2 is even, their signs cancel in pairs. The value is 9.

Question 8

What is 353^{5}?

  1. (a)729
  2. (b)243
  3. (c)125
  4. (d)15
Show answer

(b) 243

The exponent counts 5 equal factors of 3. Multiplying those factors gives 243. It does not mean base multiplied by exponent.

Counting arrangements: independent choices multiply

Question 9

A lock has 3 slots. Each independently accepts any of 10 symbols, with repetition allowed. How many different codes are possible?

  1. (a)30
  2. (b)13
  3. (c)59049
  4. (d)1000
Show answer

(d) 1000

Make 3 independent choices, with 10 symbols available each time. The count is 10 to power 3, giving 1000 codes.

Powers of 10: expanded form, decimals, and standard form

Question 10

Written out in full, how many digits does 10710^{7} have?

  1. (a)9
  2. (b)7
  3. (c)8
  4. (d)14
Show answer

(c) 8

The number is 1 followed by 7 zeros. Including the initial 1 gives 8 digits.

Comparing powers, adding like powers, and the two number-naming systems

Question 11

Which is greater: 626^{2} or 262^{6}?

  1. (a)626^{2}
  2. (b)They are equal.
  3. (c)262^{6}
Show answer

(c) 262^{6}

626^{2} equals 36, while 262^{6} equals 64. Comparing the values shows that 262^{6} is greater. Base size alone does not decide this.

m^a x n^a = (mn)^a, and m^a / n^a = (m/n)^a

Question 12

Which rule correctly simplifies 55×755^{5} \times 7^{5}?

  1. (a)Keep exponent 5 and multiply the bases to get 35535^{5}.
  2. (b)No -- the bases are different, so no rule applies.
  3. (c)Add the bases and keep the exponent to get 12512^{5}.
  4. (d)Multiply the bases and add the exponents to get 351035^{10}.
Show answer

(a) Keep exponent 5 and multiply the bases to get 35535^{5}.

The two powers share an exponent. Multiply their bases, 5 × 7 = 35, and keep exponent 5. The result is 35535^{5}.

n^(-a) = 1 / n^a

Question 13

Is 10−610^{-6} positive or negative, and is it bigger or smaller than 1?

  1. (a)Negative: it is −106-10^{6}.
  2. (b)Positive and bigger than 1: the base becomes −10-10, giving 1000000.
  3. (c)Positive and smaller than 1: it is 1106\frac{1}{10^{6}}.
Show answer

(c) Positive and smaller than 1: it is 1106\frac{1}{10^{6}}.

The negative exponent gives the reciprocal of 10 to power 6. Its denominator exceeds 1, so the value is positive and less than 1.

n^a / n^b = n^(a-b), and why n^0 = 1

Question 14

Write 23÷232^{3} \div 2^{3} as a power of 2, and give its value.

  1. (a)212^{1}, which is 2.
  2. (b)202^{0}, which is 1.
  3. (c)202^{0}, which is 0.
  4. (d)232^{3}, which is 8.
Show answer

(b) 202^{0}, which is 1.

A nonzero number divided by itself is 1. Subtracting equal exponents gives zero, so the quotient is 202^{0}, which is 1.

n^a x n^b = n^(a+b)

Question 15

Write 34×33^{4} \times 3 as a single power of 3.

  1. (a)383^{8}
  2. (b)353^{5}
  3. (c)343^{4}
  4. (d)333^{3}
Show answer

(b) 353^{5}

The lone base contributes one extra factor. Add 1 to the exponent 4, giving 353^{5}.

Common misconception in Power Play

Open full misconception guide →

What does an exponent count?

Wrong

2³ = 6

Why it feels right. I multiplied the base by the exponent.

Right

The exponent counts equal factors.

Worked example

2³
2×2×2
8
The exponent tells you how many copies of 2 to multiply.
  1. Write 2³ as 2 × 2 × 2.
  2. There are three factors and the product is 8.