Algebra Examples

${(5 x^{- \frac{3}{2}} y^{\frac{4}{3}})}^{- 6}$

Step 1

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

${(5 \frac{1}{x^{\frac{3}{2}}} y^{\frac{4}{3}})}^{- 6}$

Step 2

Combine $5$ and $\frac{1}{x^{\frac{3}{2}}}$ .

${(\frac{5}{x^{\frac{3}{2}}} y^{\frac{4}{3}})}^{- 6}$

Step 3

Combine $\frac{5}{x^{\frac{3}{2}}}$ and $y^{\frac{4}{3}}$ .

${(\frac{5 y^{\frac{4}{3}}}{x^{\frac{3}{2}}})}^{- 6}$

Step 4

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

${(\frac{x^{\frac{3}{2}}}{5 y^{\frac{4}{3}}})}^{6}$

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 $\frac{x^{\frac{3}{2}}}{5 y^{\frac{4}{3}}}$ .

$\frac{{(x^{\frac{3}{2}})}^{6}}{{(5 y^{\frac{4}{3}})}^{6}}$

Step 5.2

Apply the product rule to $5 y^{\frac{4}{3}}$ .

$\frac{{(x^{\frac{3}{2}})}^{6}}{5^{6} {(y^{\frac{4}{3}})}^{6}}$

Step 6

Multiply the exponents in ${(x^{\frac{3}{2}})}^{6}$ .

Tap for more steps...

Step 6.1

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

$\frac{x^{\frac{3}{2} \cdot 6}}{5^{6} {(y^{\frac{4}{3}})}^{6}}$

Step 6.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.2.1

Factor $2$ out of $6$ .

$\frac{x^{\frac{3}{2} \cdot (2 (3))}}{5^{6} {(y^{\frac{4}{3}})}^{6}}$

Step 6.2.2

Cancel the common factor.

$\frac{x^{\frac{3}{2} \cdot (2 \cdot 3)}}{5^{6} {(y^{\frac{4}{3}})}^{6}}$

Step 6.2.3

Rewrite the expression.

$\frac{x^{3 \cdot 3}}{5^{6} {(y^{\frac{4}{3}})}^{6}}$

Step 6.3

Multiply $3$ by $3$ .

$\frac{x^{9}}{5^{6} {(y^{\frac{4}{3}})}^{6}}$

Step 7

Simplify the denominator.

Tap for more steps...

Step 7.1

Raise $5$ to the power of $6$ .

$\frac{x^{9}}{15625 {(y^{\frac{4}{3}})}^{6}}$

Step 7.2

Multiply the exponents in ${(y^{\frac{4}{3}})}^{6}$ .

Tap for more steps...

Step 7.2.1

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

$\frac{x^{9}}{15625 y^{\frac{4}{3} \cdot 6}}$

Step 7.2.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 7.2.2.1

Factor $3$ out of $6$ .

$\frac{x^{9}}{15625 y^{\frac{4}{3} \cdot (3 (2))}}$

Step 7.2.2.2

Cancel the common factor.

$\frac{x^{9}}{15625 y^{\frac{4}{3} \cdot (3 \cdot 2)}}$

Step 7.2.2.3

Rewrite the expression.

$\frac{x^{9}}{15625 y^{4 \cdot 2}}$

Step 7.2.3

Multiply $4$ by $2$ .

$\frac{x^{9}}{15625 y^{8}}$