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Exercise

$\frac{\left(8\sin\left(x\right)^5\right)}{\sqrt{x}^4}$

Step-by-step Solution

1

Simplify $\left(\sqrt{x}\right)^4$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2}$ and $n$ equals $4$

$\frac{8\sin\left(x\right)^5}{x^{4\left(\frac{1}{2}\right)}}$
2

Multiply the fraction and term in $4\left(\frac{1}{2}\right)$

$\frac{8\sin\left(x\right)^5}{x^{\frac{4}{2}}}$
3

Divide $4$ by $2$

$\frac{8\sin\left(x\right)^5}{x^{2}}$

Final answer to the exercise

$\frac{8\sin\left(x\right)^5}{x^{2}}$

Try other ways to solve this exercise

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Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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