Basic Math Examples

$9 {(a^{\frac{2}{3}} b^{- \frac{1}{4}})}^{- \frac{3}{4}}$

Step 1

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

$9 {(a^{\frac{2}{3}} \frac{1}{b^{\frac{1}{4}}})}^{- \frac{3}{4}}$

Step 2

Combine $a^{\frac{2}{3}}$ and $\frac{1}{b^{\frac{1}{4}}}$ .

$9 {(\frac{a^{\frac{2}{3}}}{b^{\frac{1}{4}}})}^{- \frac{3}{4}}$

Step 3

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

$9 {(\frac{b^{\frac{1}{4}}}{a^{\frac{2}{3}}})}^{\frac{3}{4}}$

Step 4

Apply basic rules of exponents.

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Step 4.1

Apply the product rule to $\frac{b^{\frac{1}{4}}}{a^{\frac{2}{3}}}$ .

$9 \frac{{(b^{\frac{1}{4}})}^{\frac{3}{4}}}{{(a^{\frac{2}{3}})}^{\frac{3}{4}}}$

Step 4.2

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

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Step 4.2.1

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

$9 \frac{b^{\frac{1}{4} \cdot \frac{3}{4}}}{{(a^{\frac{2}{3}})}^{\frac{3}{4}}}$

Step 4.2.2

Multiply $\frac{1}{4} \cdot \frac{3}{4}$ .

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Step 4.2.2.1

Multiply $\frac{1}{4}$ by $\frac{3}{4}$ .

$9 \frac{b^{\frac{3}{4 \cdot 4}}}{{(a^{\frac{2}{3}})}^{\frac{3}{4}}}$

Step 4.2.2.2

Multiply $4$ by $4$ .

$9 \frac{b^{\frac{3}{16}}}{{(a^{\frac{2}{3}})}^{\frac{3}{4}}}$

Step 4.3

Multiply the exponents in ${(a^{\frac{2}{3}})}^{\frac{3}{4}}$ .

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Step 4.3.1

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

$9 \frac{b^{\frac{3}{16}}}{a^{\frac{2}{3} \cdot \frac{3}{4}}}$

Step 4.3.2

Cancel the common factor of $2$ .

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Step 4.3.2.1

Factor $2$ out of $4$ .

$9 \frac{b^{\frac{3}{16}}}{a^{\frac{2}{3} \cdot \frac{3}{2 (2)}}}$

Step 4.3.2.2

Cancel the common factor.

$9 \frac{b^{\frac{3}{16}}}{a^{\frac{2}{3} \cdot \frac{3}{2 \cdot 2}}}$

Step 4.3.2.3

Rewrite the expression.

$9 \frac{b^{\frac{3}{16}}}{a^{\frac{1}{3} \cdot \frac{3}{2}}}$

Step 4.3.3

Cancel the common factor of $3$ .

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Step 4.3.3.1

Cancel the common factor.

$9 \frac{b^{\frac{3}{16}}}{a^{\frac{1}{3} \cdot \frac{3}{2}}}$

Step 4.3.3.2

Rewrite the expression.

$9 \frac{b^{\frac{3}{16}}}{a^{\frac{1}{2}}}$

Step 5

Combine $9$ and $\frac{b^{\frac{3}{16}}}{a^{\frac{1}{2}}}$ .

$\frac{9 b^{\frac{3}{16}}}{a^{\frac{1}{2}}}$