Pre-Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

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

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

Step 1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.3

Combine $- 1$ and $\frac{3}{3}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Multiply $- 1$ by $3$ .

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

Step 1.5.2

Subtract $3$ from $2$ .

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

Step 1.6

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.4.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

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

Step 3.4.2

Multiply $3$ by $2$ .

$y^{- \frac{2}{6} + \frac{1}{2} \cdot \frac{3}{3}}$

Step 3.4.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$y^{- \frac{2}{6} + \frac{3}{2 \cdot 3}}$

Step 3.4.4

Multiply $2$ by $3$ .

$y^{- \frac{2}{6} + \frac{3}{6}}$

Step 3.5

Combine the numerators over the common denominator.

$y^{\frac{- 2 + 3}{6}}$

Step 3.6

Add $- 2$ and $3$ .

$y^{\frac{1}{6}}$