Algebra Examples

$y^{- \frac{5}{2}} \cdot y^{- 1}$

Step 1

Multiply $y^{- \frac{5}{2}}$ 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.

$y^{- \frac{5}{2} - 1}$

Step 1.2

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

$y^{- \frac{5}{2} - 1 \cdot \frac{2}{2}}$

Step 1.3

Combine $- 1$ and $\frac{2}{2}$ .

$y^{- \frac{5}{2} + \frac{- 1 \cdot 2}{2}}$

Step 1.4

Combine the numerators over the common denominator.

$y^{\frac{- 5 - 1 \cdot 2}{2}}$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Multiply $- 1$ by $2$ .

$y^{\frac{- 5 - 2}{2}}$

Step 1.5.2

Subtract $2$ from $- 5$ .

$y^{\frac{- 7}{2}}$

Step 1.6

Move the negative in front of the fraction.

$y^{- \frac{7}{2}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{y^{\frac{7}{2}}}$