Basic Math Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $a^{\frac{1}{5}} b^{5}$ .

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

Step 2.2

Multiply the exponents in ${(a^{\frac{1}{5}})}^{\frac{5}{4}}$ .

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.2.1

Cancel the common factor.

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

Step 2.2.2.2

Rewrite the expression.

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

Step 2.3

Multiply the exponents in ${(b^{5})}^{\frac{5}{4}}$ .

Tap for more steps...

Step 2.3.1

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

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

Step 2.3.2

Multiply $5 (\frac{5}{4})$ .

Tap for more steps...

Step 2.3.2.1

Combine $5$ and $\frac{5}{4}$ .

$\frac{1}{a^{\frac{1}{4}} b^{\frac{5 \cdot 5}{4}}}$

Step 2.3.2.2

Multiply $5$ by $5$ .

$\frac{1}{a^{\frac{1}{4}} b^{\frac{25}{4}}}$