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Exercise

$\sqrt[10]{x^{37}}$

Step-by-step Solution

1

Simplify $\sqrt{x^{37}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $37$ and $n$ equals $\frac{1}{10}$

$x^{37\cdot \left(\frac{1}{10}\right)}$
2

Multiply the fraction and term in $37\cdot \left(\frac{1}{10}\right)$

$\sqrt[10]{x^{37}}$

Final answer to the exercise

$\sqrt[10]{x^{37}}$

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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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