Algebra Examples

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

Step 1

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

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Step 1.1

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

$b^{- \frac{3}{4} \cdot \frac{2}{3}}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$b^{\frac{- 3}{4} \cdot \frac{2}{3}}$

Step 1.2.2

Factor $3$ out of $- 3$ .

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

Step 1.2.3

Cancel the common factor.

$b^{\frac{3 \cdot - 1}{4} \cdot \frac{2}{3}}$

Step 1.2.4

Rewrite the expression.

$b^{\frac{- 1}{4} \cdot 2}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $4$ .

$b^{\frac{- 1}{2 (2)} \cdot 2}$

Step 1.3.2

Cancel the common factor.

$b^{\frac{- 1}{2 \cdot 2} \cdot 2}$

Step 1.3.3

Rewrite the expression.

$b^{\frac{- 1}{2}}$

Step 1.4

Move the negative in front of the fraction.

$b^{- \frac{1}{2}}$

Step 2

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

$\frac{1}{b^{\frac{1}{2}}}$