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Exercise

$\left(x^{\frac{1}{2}}\right)^{\frac{5}{3}}$

Step-by-step Solution

1

Simplify $\sqrt[3]{\left(\sqrt{x}\right)^{5}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2}$ and $n$ equals $\frac{5}{3}$

$x^{\frac{1}{2}\cdot \frac{5}{3}}$
2

Multiplying fractions $\frac{1}{2} \times \frac{5}{3}$

$x^{\frac{5}{2\cdot 3}}$
3

Multiply $2$ times $3$

$\sqrt[6]{x^{5}}$

Final answer to the exercise

$\sqrt[6]{x^{5}}$

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Similar Questions Solved

$\sqrt[4]{x^3}$

$\left(2^3\right)^2$

$\left(5^3\right)^4$

$\sqrt[3]{x^3}$

$\left(2^2\right)^4$

$\left(3^2\right)^3$

$\sqrt[5]{x^3}$

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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