Simplify square root of 75x^2y^-4

$\sqrt{75 x^{2} y^{- 4}}$

Step 1

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

$\sqrt{75 x^{2} \frac{1}{y^{4}}}$

Step 2

Combine exponents.

Combine $75$ and $\frac{1}{y^{4}}$ .

$\sqrt{x^{2} \frac{75}{y^{4}}}$

Combine $x^{2}$ and $\frac{75}{y^{4}}$ .

$\sqrt{\frac{x^{2} \cdot 75}{y^{4}}}$

Step 3

Move $75$ to the left of $x^{2}$ .

$\sqrt{\frac{75 \cdot x^{2}}{y^{4}}}$

Step 4

Rewrite $\frac{75 x^{2}}{y^{4}}$ as ${(\frac{5 x}{y^{2}})}^{2} \cdot 3$ .

Factor the perfect power ${(5 x)}^{2}$ out of $75 x^{2}$ .

$\sqrt{\frac{{(5 x)}^{2} \cdot 3}{y^{4}}}$

Factor the perfect power ${(y^{2})}^{2}$ out of $y^{4}$ .

$\sqrt{\frac{{(5 x)}^{2} \cdot 3}{{(y^{2})}^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(5 x)}^{2} \cdot 3}{{(y^{2})}^{2} \cdot 1}$ .

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

Step 5

Pull terms out from under the radical.

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

Step 6

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

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