Express 32000 as a product of powers of prime factors.

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Question

Express 32000 as a product of powers of prime factors.

Options:

A .

2^{8} \times 5^{2}

B .

2^{8} \times 5^{3}

C .

2^{7} \times 5^{4}

D .

2^{8} \times 5^{4}

Answer: Option B
:
B

32000 can be written as
$32000 = (2 \times 2 \times 2 \times 2 \times 2) \times 1000 = 2^{5} \times 10^{3}$
$(a s 32 = 2 \times 2 \times 2 \times 2 \times 2)$

= $2^{5} \times (2 \times 2 \times 2 \times 5 \times 5 \times 5)$
= $2^{5} \times 2^{3} \times 5^{3}$
= $2^{8} \times 5^{3}$

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