Basic Math Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 4

Move $4$ to the left of $a^{2}$ .

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

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

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

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

Step 5.2

Apply the product rule to $4 a^{2}$ .

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

Step 6

Simplify the numerator.

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Step 6.1

Rewrite $4$ as $2^{2}$ .

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

Step 6.2

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

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

Step 6.3

Cancel the common factor of $2$ .

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Step 6.3.1

Cancel the common factor.

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

Step 6.3.2

Rewrite the expression.

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

Step 6.4

Evaluate the exponent.

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

Step 6.5

Multiply the exponents in ${(a^{2})}^{\frac{1}{2}}$ .

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Step 6.5.1

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

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

Step 6.5.2

Cancel the common factor of $2$ .

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Step 6.5.2.1

Cancel the common factor.

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

Step 6.5.2.2

Rewrite the expression.

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

Step 6.6

Simplify.

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

Step 7

Multiply the exponents in ${(b^{\frac{3}{4}})}^{\frac{1}{2}}$ .

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Step 7.1

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

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

Step 7.2

Multiply $\frac{3}{4} \cdot \frac{1}{2}$ .

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Step 7.2.1

Multiply $\frac{3}{4}$ by $\frac{1}{2}$ .

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

Step 7.2.2

Multiply $4$ by $2$ .

$\frac{2 a}{b^{\frac{3}{8}}}$