Algebra Examples

{(6^{2} - 24)}^{2} \div {(\frac{x}{y})}^{- 5}

${(6^{2} - 24)}^{2} \div {(\frac{x}{y})}^{- 5}$

Step 1

Rewrite the division as a fraction.

\frac{{(6^{2} - 24)}^{2}}{{(\frac{x}{y})}^{- 5}}

$\frac{{(6^{2} - 24)}^{2}}{{(\frac{x}{y})}^{- 5}}$

Step 2

Move

{(\frac{x}{y})}^{- 5}

${(\frac{x}{y})}^{- 5}$ to the numerator using the negative exponent rule

\frac{1}{b^{- n}} = b^{n}

$\frac{1}{b^{- n}} = b^{n}$ .

{(6^{2} - 24)}^{2} {(\frac{x}{y})}^{5}

${(6^{2} - 24)}^{2} {(\frac{x}{y})}^{5}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Raise

6

$6$ to the power of

2

$2$ .

{(36 - 24)}^{2} {(\frac{x}{y})}^{5}

${(36 - 24)}^{2} {(\frac{x}{y})}^{5}$

Step 3.2

Subtract

24

$24$ from

36

$36$ .

12^{2} {(\frac{x}{y})}^{5}

$12^{2} {(\frac{x}{y})}^{5}$

Step 3.3

Raise

12

$12$ to the power of

2

$2$ .

144 {(\frac{x}{y})}^{5}

$144 {(\frac{x}{y})}^{5}$

Step 3.4

Apply the product rule to

\frac{x}{y}

$\frac{x}{y}$ .

144 \frac{x^{5}}{y^{5}}

$144 \frac{x^{5}}{y^{5}}$

144 \frac{x^{5}}{y^{5}}

$144 \frac{x^{5}}{y^{5}}$

Step 4

Combine

144

$144$ and

\frac{x^{5}}{y^{5}}

$\frac{x^{5}}{y^{5}}$ .

\frac{144 x^{5}}{y^{5}}

$\frac{144 x^{5}}{y^{5}}$