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Exercise

$\left(8^{\frac{4}{9}}\right)^{-\frac{3}{2}}$

Step-by-step Solution

1

Simplify $\left(\sqrt[9]{\left(8\right)^{4}}\right)^{-\frac{3}{2}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{4}{9}$ and $n$ equals $-\frac{3}{2}$

$8^{\frac{4}{9}\cdot \left(-\frac{3}{2}\right)}$

Final answer to the exercise

$8^{\frac{4}{9}\cdot \left(-\frac{3}{2}\right)}$

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Main Topic: Powers of powers

When we have a power inside another power, we can simplify multiplying the exponents: $\left(x^m\right)^n=x^{m\cdot n}$.

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