Final answer to the problem
$\frac{x^2\left(1+x^2\right)^2\left(3x+7\right)}{\left(\sin\left(x^2\right)+1\right)^7\cos\left(9x+7\right)}$
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Step-by-step Solution
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1
Factor the polynomial $\left(x+x^3\right)$ by it's greatest common factor (GCF): $x$
$\frac{\left(x\left(1+x^2\right)\right)^2\left(3x+7\right)}{\left(\sin\left(x^2\right)+1\right)^7\cos\left(9x+7\right)}$
2
The power of a product is equal to the product of it's factors raised to the same power
$\frac{x^2\left(1+x^2\right)^2\left(3x+7\right)}{\left(\sin\left(x^2\right)+1\right)^7\cos\left(9x+7\right)}$
Final answer to the problem
$\frac{x^2\left(1+x^2\right)^2\left(3x+7\right)}{\left(\sin\left(x^2\right)+1\right)^7\cos\left(9x+7\right)}$