Final answer to the problem
$\frac{x^5\left(x^2+7\right)^5\sqrt{8x^2+\cos\left(x\right)}}{\left(2x^2-x+1\right)^2e^x}$
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Step-by-step Solution
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1
Factor the polynomial $\left(x^3+7x\right)$ by it's greatest common factor (GCF): $x$
$\frac{\left(x\left(x^2+7\right)\right)^5\sqrt{8x^2+\cos\left(x\right)}}{\left(2x^2-x+1\right)^2e^x}$
2
The power of a product is equal to the product of it's factors raised to the same power
$\frac{x^5\left(x^2+7\right)^5\sqrt{8x^2+\cos\left(x\right)}}{\left(2x^2-x+1\right)^2e^x}$
Final answer to the problem
$\frac{x^5\left(x^2+7\right)^5\sqrt{8x^2+\cos\left(x\right)}}{\left(2x^2-x+1\right)^2e^x}$