Simplify $\left(\frac{a^{16}}{b^{-6}}\right)^{\frac{3}{2}}$ . Answer ...

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Worked solution

1. Rewrite the expression inside the brackets using the negative index law.

$\frac{a^{16}}{b^{-6}}=a^{16}b^6$
So
$\left(\frac{a^{16}}{b^{-6}}\right)^{\frac32}=\left(a^{16}b^6\right)^{\frac32}.$

2. Raise each factor to the power $\frac32$ and multiply the indices.

$\left(a^{16}b^6\right)^{\frac32}=a^{16\times\frac32}b^{6\times\frac32}$
$=a^{24}b^9$

Answer

$a^{24}b^9$

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