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Exercise

$\left(\sqrt[3]{x}\right)^7$

Step-by-step Solution

1

Simplify $\left(\sqrt[3]{x}\right)^7$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{3}$ and $n$ equals $7$

$x^{7\left(\frac{1}{3}\right)}$
2

Multiply the fraction and term in $7\left(\frac{1}{3}\right)$

$\sqrt[3]{x^{7}}$

Final answer to the exercise

$\sqrt[3]{x^{7}}$

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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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