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, assuming positive real numbers.

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

Step 2.3

Multiply $x$ by $x^{\frac{3}{2}}$ by adding the exponents.

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Step 2.3.1

Move $x^{\frac{3}{2}}$ .

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

Step 2.3.2

Multiply $x^{\frac{3}{2}}$ by $x$ .

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Step 2.3.2.1

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

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

Step 2.3.2.2

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

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

Step 2.3.3

Write $1$ as a fraction with a common denominator.

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

Step 2.3.4

Combine the numerators over the common denominator.

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

Step 2.3.5

Add $3$ and $2$ .

$\frac{3 x^{\frac{5}{2}} y^{2}}{4 y^{4}}$

Step 3

Factor $y^{2}$ out of $3 x^{\frac{5}{2}} y^{2}$ .

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

Step 4

Cancel the common factors.

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Step 4.1

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$\frac{3 x^{\frac{5}{2}}}{4 y^{2}}$