# Step-by-step Solution

Go!
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## Final Answer

$\frac{x^5\left(x^2+7\right)^5\sqrt{8x^2+\cos\left(x\right)}}{e^x\left(2x^2-x+1\right)^2}$

## Step-by-step Solution

Problem to solve:

$\left(\frac{\left(x^3+7x\right)^5\sqrt{8x^2+cosx}}{\left(2x^2-x+1\right)^2e^x\:}\right)$

Solving method

1

Factor the polynomial $\left(x^3+7x\right)$ by it's GCF: $x$

$\frac{\left(x\left(x^2+7\right)\right)^5\sqrt{8x^2+\cos\left(x\right)}}{e^x\left(2x^2-x+1\right)^2}$
2

The power of a product is equal to the product of it's factors raised to the same power

$\frac{x^5\left(x^2+7\right)^5\sqrt{8x^2+\cos\left(x\right)}}{e^x\left(2x^2-x+1\right)^2}$

## Final Answer

$\frac{x^5\left(x^2+7\right)^5\sqrt{8x^2+\cos\left(x\right)}}{e^x\left(2x^2-x+1\right)^2}$
$\left(\frac{\left(x^3+7x\right)^5\sqrt{8x^2+cosx}}{\left(2x^2-x+1\right)^2e^x\:}\right)$

### Main topic:

Simplification of algebraic fractions

~ 0.14 s