How to simplify this?

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How to simplify this?

${(16 p^{16})}^{\frac{1}{4}}$ $(16p^16)^(1/4)$

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Answer 1 · 2016-10-26T00:27:04

${(16 p^{16})}^{\frac{1}{4}} = 2 p^{4}$ $(16p^16)^(1/4)=2p^4$

Explanation:

We will apply the following rules of exponents:

${(a b)}^{x} = a^{x} b^{x}$ $(ab)^x = a^xb^x$
${(a^{x})}^{y} = a^{x y}$ $(a^x)^y = a^(xy)$

With those, and observing that $16 = 2^{4}$ $16 = 2^4$ , we have

${(16 p^{16})}^{\frac{1}{4}} = 16^{\frac{1}{4}} {(p^{16})}^{\frac{1}{4}}$ $(16p^16)^(1/4) = 16^(1/4)(p^16)^(1/4)$

$= {(2^{4})}^{\frac{1}{4}} {(p^{16})}^{\frac{1}{4}}$ $=(2^4)^(1/4)(p^16)^(1/4)$

$= 2^{4 \cdot \frac{1}{4}} p^{16 \cdot \frac{1}{4}}$ $=2^(4*1/4)p^(16*1/4)$

$= 2^{1} p^{4}$ $=2^1p^4$

$= 2 p^{4}$ $=2p^4$

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How to simplify this?

${(16 p^{16})}^{\frac{1}{4}}$ $(16p^16)^(1/4)$

1 Answer

Explanation:

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${(16 p^{16})}^{\frac{1}{4}}$ $(16p^16)^(1/4)$