Precalculus Examples

$4 x^{\frac{1}{2}} y^{\frac{3}{4}} - 8 x^{\frac{3}{2}} y^{\frac{1}{4}}$

Step 1

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

$4 \sqrt{x^{1}} y^{\frac{3}{4}} - 8 x^{\frac{3}{2}} y^{\frac{1}{4}}$

Step 2

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

$4 \sqrt{x^{1}} \sqrt[4]{y^{3}} - 8 x^{\frac{3}{2}} y^{\frac{1}{4}}$

Step 3

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

$4 \sqrt{x^{1}} \sqrt[4]{y^{3}} - 8 \sqrt{x^{3}} y^{\frac{1}{4}}$

Step 4

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

$4 \sqrt{x^{1}} \sqrt[4]{y^{3}} - 8 \sqrt{x^{3}} \sqrt[4]{y^{1}}$

Step 5

Anything raised to $1$ is the base itself.

$4 \sqrt{x} \sqrt[4]{y^{3}} - 8 \sqrt{x^{3}} \sqrt[4]{y^{1}}$

Step 6

Anything raised to $1$ is the base itself.

$4 \sqrt{x} \sqrt[4]{y^{3}} - 8 \sqrt{x^{3}} \sqrt[4]{y}$