Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

$\frac{a^{\frac{4}{3}}}{a}$

Step 2

Move $a^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$a^{\frac{4}{3}} a^{- 1}$

Step 3

Multiply $a^{\frac{4}{3}}$ by $a^{- 1}$ by adding the exponents.

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Step 3.1

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

$a^{\frac{4}{3} - 1}$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$a^{\frac{4}{3} - 1 \cdot \frac{3}{3}}$

Step 3.3

Combine $- 1$ and $\frac{3}{3}$ .

$a^{\frac{4}{3} + \frac{- 1 \cdot 3}{3}}$

Step 3.4

Combine the numerators over the common denominator.

$a^{\frac{4 - 1 \cdot 3}{3}}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $3$ .

$a^{\frac{4 - 3}{3}}$

Step 3.5.2

Subtract $3$ from $4$ .

$a^{\frac{1}{3}}$