2 Answers

IanJ · Answer 1 · 2022-03-13T16:37:08+0000

9514 1404 393

Answer:

16

Explanation:

There are several ways to go at this. Perhaps the simplest is to put the expression into your calculator.

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Using the rules of exponents, you recognize ...

a^-b = 1/a^b

(a^b)^c = a^(bc)

(a^b)(a^c) = a^(b+c)

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So, we can rewrite the expression to be ...

$\displaystyle(1)/(2)\cdot\left((1)/(2)\right)^(-5)=2^(-1)\cdot(2^(-1))^-5\\\\=2^(-1)\cdot2^((-1)(-5))=2^(-1)\cdot2^5\\\\=2^(-1+5)=2^4=\boxed{16}$

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