Algebra Examples

${(\frac{- 8 y^{\frac{3}{4}}}{y^{3} z^{6}})}^{- \frac{1}{3}}$

Step 1

Move $y^{\frac{3}{4}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

${(\frac{- 8}{y^{3} z^{6} y^{- \frac{3}{4}}})}^{- \frac{1}{3}}$

Step 2

Multiply $y^{3}$ by $y^{- \frac{3}{4}}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $y^{- \frac{3}{4}}$ .

${(\frac{- 8}{y^{- \frac{3}{4}} y^{3} z^{6}})}^{- \frac{1}{3}}$

Step 2.2

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

${(\frac{- 8}{y^{- \frac{3}{4} + 3} z^{6}})}^{- \frac{1}{3}}$

Step 2.3

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

${(\frac{- 8}{y^{- \frac{3}{4} + 3 \cdot \frac{4}{4}} z^{6}})}^{- \frac{1}{3}}$

Step 2.4

Combine $3$ and $\frac{4}{4}$ .

${(\frac{- 8}{y^{- \frac{3}{4} + \frac{3 \cdot 4}{4}} z^{6}})}^{- \frac{1}{3}}$

Step 2.5

Combine the numerators over the common denominator.

${(\frac{- 8}{y^{\frac{- 3 + 3 \cdot 4}{4}} z^{6}})}^{- \frac{1}{3}}$

Step 2.6

Simplify the numerator.

Tap for more steps...

Step 2.6.1

Multiply $3$ by $4$ .

${(\frac{- 8}{y^{\frac{- 3 + 12}{4}} z^{6}})}^{- \frac{1}{3}}$

Step 2.6.2

Add $- 3$ and $12$ .

${(\frac{- 8}{y^{\frac{9}{4}} z^{6}})}^{- \frac{1}{3}}$

Step 3

Move the negative in front of the fraction.

${(- \frac{8}{y^{\frac{9}{4}} z^{6}})}^{- \frac{1}{3}}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

${(- \frac{y^{\frac{9}{4}} z^{6}}{8})}^{\frac{1}{3}}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 5.1

Apply the product rule to $- \frac{y^{\frac{9}{4}} z^{6}}{8}$ .

${(- 1)}^{\frac{1}{3}} {(\frac{y^{\frac{9}{4}} z^{6}}{8})}^{\frac{1}{3}}$

Step 5.2

Apply the product rule to $\frac{y^{\frac{9}{4}} z^{6}}{8}$ .

${(- 1)}^{\frac{1}{3}} \frac{{(y^{\frac{9}{4}} z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 5.3

Apply the product rule to $y^{\frac{9}{4}} z^{6}$ .

${(- 1)}^{\frac{1}{3}} \frac{{(y^{\frac{9}{4}})}^{\frac{1}{3}} {(z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 6

Simplify the expression.

Tap for more steps...

Step 6.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${({(- 1)}^{3})}^{\frac{1}{3}} \frac{{(y^{\frac{9}{4}})}^{\frac{1}{3}} {(z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(- 1)}^{3 (\frac{1}{3})} \frac{{(y^{\frac{9}{4}})}^{\frac{1}{3}} {(z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 7

Cancel the common factor of $3$ .

Tap for more steps...

Step 7.1

Cancel the common factor.

${(- 1)}^{3 (\frac{1}{3})} \frac{{(y^{\frac{9}{4}})}^{\frac{1}{3}} {(z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 7.2

Rewrite the expression.

${(- 1)}^{1} \frac{{(y^{\frac{9}{4}})}^{\frac{1}{3}} {(z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 8

Evaluate the exponent.

$- \frac{{(y^{\frac{9}{4}})}^{\frac{1}{3}} {(z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 9

Simplify the numerator.

Tap for more steps...

Step 9.1

Multiply the exponents in ${(y^{\frac{9}{4}})}^{\frac{1}{3}}$ .

Tap for more steps...

Step 9.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{y^{\frac{9}{4} \cdot \frac{1}{3}} {(z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 9.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 9.1.2.1

Factor $3$ out of $9$ .

$- \frac{y^{\frac{3 (3)}{4} \cdot \frac{1}{3}} {(z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 9.1.2.2

Cancel the common factor.

$- \frac{y^{\frac{3 \cdot 3}{4} \cdot \frac{1}{3}} {(z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 9.1.2.3

Rewrite the expression.

$- \frac{y^{\frac{3}{4}} {(z^{6})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 9.2

Multiply the exponents in ${(z^{6})}^{\frac{1}{3}}$ .

Tap for more steps...

Step 9.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{y^{\frac{3}{4}} z^{6 (\frac{1}{3})}}{8^{\frac{1}{3}}}$

Step 9.2.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 9.2.2.1

Factor $3$ out of $6$ .

$- \frac{y^{\frac{3}{4}} z^{3 (2) \frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 9.2.2.2

Cancel the common factor.

$- \frac{y^{\frac{3}{4}} z^{3 \cdot 2 \frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 9.2.2.3

Rewrite the expression.

$- \frac{y^{\frac{3}{4}} z^{2}}{8^{\frac{1}{3}}}$

Step 10

Simplify the denominator.

Tap for more steps...

Step 10.1

Rewrite $8$ as $2^{3}$ .

$- \frac{y^{\frac{3}{4}} z^{2}}{{(2^{3})}^{\frac{1}{3}}}$

Step 10.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{y^{\frac{3}{4}} z^{2}}{2^{3 (\frac{1}{3})}}$

Step 10.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 10.3.1

Cancel the common factor.

$- \frac{y^{\frac{3}{4}} z^{2}}{2^{3 (\frac{1}{3})}}$

Step 10.3.2

Rewrite the expression.

$- \frac{y^{\frac{3}{4}} z^{2}}{2^{1}}$

Step 10.4

Evaluate the exponent.

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

Step 11

Reorder factors in $- \frac{y^{\frac{3}{4}} z^{2}}{2}$ .

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