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# What is the value of 8^3*32^2*16^(-4)?

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Re: What is the value of 8^3*32^2*16^(-4)? [#permalink]
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Bunuel wrote:
What is the value of $$8^3*32^2*16^{(-4)}$$?

A. 1/8
B. 1/2
C. 2
D. 8
E. 8^3

Let’s re-express each number with a base of 2; thus, 8^3 = (2^3)^3 = 2^9. We see that 32^2 = (2^5)^2 = 2^10, and 16^-4 = (2^4)^-4 = 2^-16. Thus, we have:

2^9 x 2^10 x 2^-16

2^(9 + 10 - 16) = 2^3 = 8

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What is the value of 8^3*32^2*16^(-4)? [#permalink]
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Solution

To find
We need to determine
• The value of the given expression $$8^3 ∗ 32^2 ∗16^{(−4)}$$

Approach and Working out
Simplifying the given expression, we get:
• $$8^3 ∗ 32^2 ∗16^{(−4)}$$
= $$(2^3)^3 * (2^5)^2 * (2^4)^{(-4)}$$
= $$2^9 * 2^{10} * 2^{-16}$$
= $$2^{9+10-16}$$
= $$2^3$$
= 8

Thus, option D is the correct answer.

Correct Answer: Option D
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Re: What is the value of 8^3*32^2*16^(-4)? [#permalink]
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Re: What is the value of 8^3*32^2*16^(-4)? [#permalink]
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