How do you simplify ${(16 a^{4})}^{\frac{3}{2}}$ $(16a^4)^(3/2)$ ?

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How do you simplify ${(16 a^{4})}^{\frac{3}{2}}$ $(16a^4)^(3/2)$ ?

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Answer 1 · 2016-02-29T13:32:44

$64 a^{6}$ $64a^6$

Explanation:

To simplify ${(16 a^{4})}^{\frac{3}{2}}$ $(16a^4)^(3/2)$ , remember the identity ${(a^{m})}^{n} = a^{m n}$ $(a^m)^n=a^(mn)$ and ${(a b)}^{m} = a^{m} \times b^{m}$ $(ab)^m=a^mxxb^m$

Hence, ${(16 a^{4})}^{\frac{3}{2}} = 16^{\frac{3}{2}} \times a^{4 \times (\frac{3}{2})}$ $(16a^4)^(3/2)=16^(3/2)xxa^(4xx(3/2))$ , but $16 = 2^{4}$ $16=2^4$

Hence this is ${(2^{4})}^{\frac{3}{2}} \times a^{6}$ $(2^4)^(3/2)xxa^6$

or $2^{(4 \times \frac{3}{2})} \times (a^{6})$ $2^((4xx3/2))xx(a^6)$

or $2^{6} \cdot a^{6} = 64 a^{6}$ $2^6*a^6=64a^6$

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How do you simplify ${(16 a^{4})}^{\frac{3}{2}}$ $(16a^4)^(3/2)$ ?

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