Algebra Examples

$\frac{\sqrt{9 x^{2} y^{4}}}{4 x^{- \frac{3}{2}} y^{4}}$

Step 1

Move $x^{- \frac{3}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{\sqrt{9 x^{2} y^{4}} x^{\frac{3}{2}}}{4 y^{4}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $9 x^{2} y^{4}$ as ${(3 x y^{2})}^{2}$ .

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

Step 2.2

Pull terms out from under the radical.

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

Step 2.3

Remove non-negative terms from the absolute value.

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

Step 3

Factor $y^{2}$ out of $3 y^{2} | x | x^{\frac{3}{2}}$ .

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

Step 4

Cancel the common factors.

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Step 4.1

Factor $y^{2}$ out of $4 y^{4}$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Reorder factors in $\frac{3 | x | x^{\frac{3}{2}}}{4 y^{2}}$ .

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