Algebra Examples

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

Step 1

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

$\frac{3 x^{2} y^{\frac{3}{2}} y^{- \frac{1}{2}}}{x}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $y^{\frac{3}{2}}$ by $y^{- \frac{1}{2}}$ by adding the exponents.

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Step 2.1.1

Move $y^{- \frac{1}{2}}$ .

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

Step 2.1.2

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

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

Step 2.1.3

Combine the numerators over the common denominator.

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

Step 2.1.4

Add $- 1$ and $3$ .

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

Step 2.1.5

Divide $2$ by $2$ .

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

Step 2.2

Simplify $3 x^{2} y^{1}$ .

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

Step 3

Cancel the common factor of $x^{2}$ and $x$ .

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Step 3.1

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

$\frac{x (3 x y)}{x}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Factor $x$ out of $x^{1}$ .

$\frac{x (3 x y)}{x \cdot 1}$

Step 3.2.3

Cancel the common factor.

$\frac{x (3 x y)}{x \cdot 1}$

Step 3.2.4

Rewrite the expression.

$\frac{3 x y}{1}$

Step 3.2.5

Divide $3 x y$ by $1$ .

$3 x y$