Precalculus Examples

$\frac{{(2 x^{3})}^{2} z^{5}}{2 z^{9}}$

Step 1

Cancel the common factor of $z^{5}$ and $z^{9}$ .

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Step 1.1

Factor $z^{5}$ out of ${(2 x^{3})}^{2} z^{5}$ .

$\frac{z^{5} {(2 x^{3})}^{2}}{2 z^{9}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $z^{5}$ out of $2 z^{9}$ .

$\frac{z^{5} {(2 x^{3})}^{2}}{z^{5} (2 z^{4})}$

Step 1.2.2

Cancel the common factor.

$\frac{z^{5} {(2 x^{3})}^{2}}{z^{5} (2 z^{4})}$

Step 1.2.3

Rewrite the expression.

$\frac{{(2 x^{3})}^{2}}{2 z^{4}}$

$\frac{{(2 x^{3})}^{2}}{2 z^{4}}$

$\frac{{(2 x^{3})}^{2}}{2 z^{4}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $2 x^{3}$ .

$\frac{2^{2} {(x^{3})}^{2}}{2 z^{4}}$

Step 2.2

Raise $2$ to the power of $2$ .

$\frac{4 {(x^{3})}^{2}}{2 z^{4}}$

Step 2.3

Multiply the exponents in ${(x^{3})}^{2}$ .

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Step 2.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4 x^{3 \cdot 2}}{2 z^{4}}$

Step 2.3.2

Multiply $3$ by $2$ .

$\frac{4 x^{6}}{2 z^{4}}$

$\frac{4 x^{6}}{2 z^{4}}$

$\frac{4 x^{6}}{2 z^{4}}$

Step 3

Cancel the common factor of $4$ and $2$ .

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Step 3.1

Factor $2$ out of $4 x^{6}$ .

$\frac{2 (2 x^{6})}{2 z^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2 z^{4}$ .

$\frac{2 (2 x^{6})}{2 (z^{4})}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (2 x^{6})}{2 z^{4}}$

Step 3.2.3

Rewrite the expression.

$\frac{2 x^{6}}{z^{4}}$

$\frac{2 x^{6}}{z^{4}}$

$\frac{2 x^{6}}{z^{4}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$