Calculus Examples

$\sqrt{81 x^{10} y^{- 6}}$

Step 1

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

$\sqrt{81 x^{10} \frac{1}{y^{6}}}$

Step 2

Combine exponents.

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Step 2.1

Combine $81$ and $\frac{1}{y^{6}}$ .

$\sqrt{x^{10} \frac{81}{y^{6}}}$

Step 2.2

Combine $x^{10}$ and $\frac{81}{y^{6}}$ .

$\sqrt{\frac{x^{10} \cdot 81}{y^{6}}}$

Step 3

Move $81$ to the left of $x^{10}$ .

$\sqrt{\frac{81 \cdot x^{10}}{y^{6}}}$

Step 4

Rewrite $81 x^{10}$ as ${(9 x^{5})}^{2}$ .

$\sqrt{\frac{{(9 x^{5})}^{2}}{y^{6}}}$

Step 5

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

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

Step 6

Rewrite $\frac{{(9 x^{5})}^{2}}{{(y^{3})}^{2}}$ as ${(\frac{9 x^{5}}{y^{3}})}^{2}$ .

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

Step 7

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

$\frac{9 x^{5}}{y^{3}}$