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Exercise

$\frac{4x^{\frac{11}{20}}\sqrt[5]{x^2}}{x^2z}$

Step-by-step Solution

1

Simplify $\sqrt[5]{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{5}$

$\frac{4\sqrt[20]{x^{11}}\sqrt[5]{x^{2}}}{x^2z}$
2

When multiplying exponents with same base we can add the exponents

$\frac{4\sqrt[20]{x^{19}}}{x^2z}$
3

Simplify the fraction by $x$

$\frac{4}{x^{\frac{-19+2\cdot 20}{20}}z}$
4

Multiply $2$ times $20$

$\frac{4}{x^{\frac{-19+40}{20}}z}$
5

Subtract the values $40$ and $-19$

$\frac{4}{\sqrt[20]{x^{21}}z}$

Final answer to the exercise

$\frac{4}{\sqrt[20]{x^{21}}z}$

Try other ways to solve this exercise

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  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
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Main Topic: Factorization

In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.

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