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Problems based on Numbers Test 4

Question : 16 of 40

Marks: +1, -0

8^7 \times 11^2 \times 14^3 \times 15^4

Solution:

Concept:

Total prime factors are found by prime factorising the expression and adding all exponents.

Explanation:

Given expression:

8^7 \times 11^2 \times 14^3 \times 15^4

Break each composite number into primes:

8=2^3

14=2\times 7

15=3\times 5

So,

8^7 \times 11^2 \times 14^3 \times 15^4 = (2^3)^7 \times 11^2 \times (2\times 7)^3 \times (3\times 5)^4

Simplify powers:

= 2^{21} \times 11^2 \times 2^3 \times 7^3 \times 3^4 \times 5^4

Combine same bases:

= 2^{24} \times 3^4 \times 5^4 \times 7^3 \times 11^2

Total prime factors = sum of exponents:

24+4+4+3+2=37

Answer:

37

, which matches option B.

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