Algebra Examples

${(\frac{b^{\frac{4}{5}}}{b^{7}})}^{- 5}$

Step 1

Move $b^{\frac{4}{5}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

${(\frac{1}{b^{7} b^{- \frac{4}{5}}})}^{- 5}$

Step 2

Multiply $b^{7}$ by $b^{- \frac{4}{5}}$ by adding the exponents.

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Step 2.1

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

${(\frac{1}{b^{7 - \frac{4}{5}}})}^{- 5}$

Step 2.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

${(\frac{1}{b^{7 \cdot \frac{5}{5} - \frac{4}{5}}})}^{- 5}$

Step 2.3

Combine $7$ and $\frac{5}{5}$ .

${(\frac{1}{b^{\frac{7 \cdot 5}{5} - \frac{4}{5}}})}^{- 5}$

Step 2.4

Combine the numerators over the common denominator.

${(\frac{1}{b^{\frac{7 \cdot 5 - 4}{5}}})}^{- 5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $7$ by $5$ .

${(\frac{1}{b^{\frac{35 - 4}{5}}})}^{- 5}$

Step 2.5.2

Subtract $4$ from $35$ .

${(\frac{1}{b^{\frac{31}{5}}})}^{- 5}$

Step 3

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

${(b^{\frac{31}{5}})}^{5}$

Step 4

Multiply the exponents in ${(b^{\frac{31}{5}})}^{5}$ .

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Step 4.1

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

$b^{\frac{31}{5} \cdot 5}$

Step 4.2

Cancel the common factor of $5$ .

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Step 4.2.1

Cancel the common factor.

$b^{\frac{31}{5} \cdot 5}$

Step 4.2.2

Rewrite the expression.

$b^{31}$