Precalculus Examples

$\sqrt[4]{{(3 x^{5} y^{- 2})}^{4}}$

Step 1

Pull terms out from under the radical, assuming positive real numbers.

$3 x^{5} y^{- 2}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 x^{5} \frac{1}{y^{2}}$

Step 3

Multiply $3 x^{5} \frac{1}{y^{2}}$ .

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Step 3.1

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

$x^{5} \frac{3}{y^{2}}$

Step 3.2

Combine $x^{5}$ and $\frac{3}{y^{2}}$ .

$\frac{x^{5} \cdot 3}{y^{2}}$

Step 4

Move $3$ to the left of $x^{5}$ .

$\frac{3 x^{5}}{y^{2}}$