Class 7 Prime Factors in Exponent Form — practice questions with answers

Number System · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. In the power

3^{4}

, which number is the base?

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Answer: B) 3

3^{4}

the base is 3 (the number multiplied) and the exponent is 4 (how many times it is used).

3^{4} = 3 \times 3 \times 3 \times 3 = 81

2. The factor tree for 84 has one box empty. Use it to write 84 as a product of powers of primes.

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Answer: A)

2^{2} \times 3 \times 7

The empty box is 21 ÷ 3 = 7. The prime leaves are 2, 2, 3 and 7, so 84 =

2^{2} \times 3 \times 7

2^{2} \times 21

stops early because 21 is not prime.

3. The prime factorisation of a number N is

2 \times 3^{2} \times 5

. What is N?

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Answer: B) 90

N = 2 × 9 × 5 = 90. Using 3 instead of

3^{2}

gives 30.

4. In the division ladder for 360, one divisor is hidden. What is 360 as a product of powers of primes?

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Answer: C)

2^{3} \times 3^{2} \times 5

The hidden divisor takes 15 to 5, so it is 3. The divisors are 2, 2, 2, 3, 3, 5, giving 360 =

2^{3} \times 3^{2} \times 5

(8 × 9 × 5 = 360).

5. Pooja knows that every pair of 2 and 5 makes a 10. How many zeros are at the end of

2^{6} \times 5^{4}

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Answer: A) 4

Only 4 pairs of (2, 5) can be made, since there are just four 5s:

2^{6} \times 5^{4} = 2^{2} \times 1 0^{4} = 40000

. It ends in 4 zeros.

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