Algebra Examples

${(\frac{p^{\frac{2}{3}}}{q^{\frac{1}{2}}})}^{- \frac{2}{3}}$

Step 1

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

${(\frac{q^{\frac{1}{2}}}{p^{\frac{2}{3}}})}^{\frac{2}{3}}$

Step 2

Apply the product rule to $\frac{q^{\frac{1}{2}}}{p^{\frac{2}{3}}}$ .

$\frac{{(q^{\frac{1}{2}})}^{\frac{2}{3}}}{{(p^{\frac{2}{3}})}^{\frac{2}{3}}}$

Step 3

Multiply the exponents in ${(q^{\frac{1}{2}})}^{\frac{2}{3}}$ .

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Step 3.1

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

$\frac{q^{\frac{1}{2} \cdot \frac{2}{3}}}{{(p^{\frac{2}{3}})}^{\frac{2}{3}}}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Cancel the common factor.

$\frac{q^{\frac{1}{2} \cdot \frac{2}{3}}}{{(p^{\frac{2}{3}})}^{\frac{2}{3}}}$

Step 3.2.2

Rewrite the expression.

$\frac{q^{\frac{1}{3}}}{{(p^{\frac{2}{3}})}^{\frac{2}{3}}}$

Step 4

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

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Step 4.1

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

$\frac{q^{\frac{1}{3}}}{p^{\frac{2}{3} \cdot \frac{2}{3}}}$

Step 4.2

Multiply $\frac{2}{3} \cdot \frac{2}{3}$ .

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Step 4.2.1

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

$\frac{q^{\frac{1}{3}}}{p^{\frac{2 \cdot 2}{3 \cdot 3}}}$

Step 4.2.2

Multiply $2$ by $2$ .

$\frac{q^{\frac{1}{3}}}{p^{\frac{4}{3 \cdot 3}}}$

Step 4.2.3

Multiply $3$ by $3$ .

$\frac{q^{\frac{1}{3}}}{p^{\frac{4}{9}}}$