Basic Math Examples

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

Step 1

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

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

Step 2

Combine $\frac{1}{a^{\frac{5}{4}}}$ and $b^{\frac{1}{4}}$ .

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

Step 3

Apply basic rules of exponents.

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Step 3.1

Apply the product rule to $\frac{b^{\frac{1}{4}}}{a^{\frac{5}{4}}}$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Combine $\frac{1}{4}$ and $5$ .

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

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Multiply $\frac{5}{4} \cdot 5$ .

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Step 3.3.2.1

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

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

Step 3.3.2.2

Multiply $5$ by $5$ .

$\frac{b^{\frac{5}{4}}}{a^{\frac{25}{4}}}$