Algebra Examples

$\frac{\sqrt{9 x^{2} y}}{2 x^{- 4} y^{2}}$

Step 1

Move $x^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{\sqrt{9 x^{2} y} x^{4}}{2 y^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

Rewrite $9$ as $3^{2}$ .

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

Step 2.1.2

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

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

Step 2.2

Pull terms out from under the radical.

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

Step 2.3

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 2.3.1

Move $x^{4}$ .

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

Step 2.3.2

Multiply $x^{4}$ by $x$ .

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Step 2.3.2.1

Raise $x$ to the power of $1$ .

$\frac{3 (x^{4} x^{1}) \sqrt{y}}{2 y^{2}}$

Step 2.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.3.3

Add $4$ and $1$ .

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