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Exercise

$\sqrt[m+1]{3^{3m+1}}$

Step-by-step Solution

1

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

$3^{\left(3m+1\right)\frac{1}{m+1}}$

Final answer to the exercise

$3^{\left(3m+1\right)\frac{1}{m+1}}$

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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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