Basic Math Examples

$\frac{4 y^{2}}{2 y^{\frac{1}{2}}}$

Step 1

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

$\frac{4 y^{2} y^{- \frac{1}{2}}}{2}$

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

$\frac{4 y^{- \frac{1}{2} + 2}}{2}$

Step 2.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 y^{- \frac{1}{2} + 2 \cdot \frac{2}{2}}}{2}$

Step 2.4

Combine $2$ and $\frac{2}{2}$ .

$\frac{4 y^{- \frac{1}{2} + \frac{2 \cdot 2}{2}}}{2}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{4 y^{\frac{- 1 + 2 \cdot 2}{2}}}{2}$

Step 2.6

Simplify the numerator.

Tap for more steps...

Step 2.6.1

Multiply $2$ by $2$ .

$\frac{4 y^{\frac{- 1 + 4}{2}}}{2}$

Step 2.6.2

Add $- 1$ and $4$ .

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

Step 3

Factor $2$ out of $4 y^{\frac{3}{2}}$ .

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

Step 4

Cancel the common factors.

Tap for more steps...

Step 4.1

Factor $2$ out of $2$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 4.4

Divide $2 y^{\frac{3}{2}}$ by $1$ .

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