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Exercise

$\left(x^2+4x+4\right)^{\left(x^2+6x+6\right)}^{-6}$

Step-by-step Solution

1

Simplify $\left(\left(x^2+4x+4\right)^{\left(x^2+6x+6\right)}\right)^{-6}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $x^2+6x+6$ and $n$ equals $-6$

$\left(x^2+4x+4\right)^{-6\left(x^2+6x+6\right)}$

Final answer to the exercise

$\left(x^2+4x+4\right)^{-6\left(x^2+6x+6\right)}$

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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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