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Exercise

$\left(sen^4x\right)^{e^{2x}}$

Step-by-step Solution

1

Simplify $\left(\sin\left(x\right)^4\right)^{\left(e^{2x}\right)}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4$ and $n$ equals $e^{2x}$

$\sin\left(x\right)^{4e^{2x}}$

Final answer to the exercise

$\sin\left(x\right)^{4e^{2x}}$

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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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