Precalculus Examples

$\frac{x^{\frac{1}{2}}}{y^{\frac{1}{2}}} \cdot z^{\frac{1}{3}}$

Step 1

Combine $\frac{x^{\frac{1}{2}}}{y^{\frac{1}{2}}}$ and $z^{\frac{1}{3}}$ .

$\frac{x^{\frac{1}{2}} z^{\frac{1}{3}}}{y^{\frac{1}{2}}}$

Step 2

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\frac{\sqrt{x^{1}} z^{\frac{1}{3}}}{y^{\frac{1}{2}}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\frac{\sqrt{x^{1}} \sqrt[3]{z^{1}}}{y^{\frac{1}{2}}}$

Step 4

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\frac{\sqrt{x^{1}} \sqrt[3]{z^{1}}}{\sqrt{y^{1}}}$

Step 5

Anything raised to $1$ is the base itself.

$\frac{\sqrt{x} \sqrt[3]{z^{1}}}{\sqrt{y^{1}}}$

Step 6

Anything raised to $1$ is the base itself.

$\frac{\sqrt{x} \sqrt[3]{z}}{\sqrt{y^{1}}}$

Step 7

Anything raised to $1$ is the base itself.

$\frac{\sqrt{x} \sqrt[3]{z}}{\sqrt{y}}$

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