Basic Math Examples

$\frac{a^{\frac{5}{3}} b^{\frac{4}{3}}}{a^{- \frac{4}{3}} b^{\frac{1}{3}}}$

Step 1

Move $a^{- \frac{4}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{\frac{5}{3}} b^{\frac{4}{3}} a^{\frac{4}{3}}}{b^{\frac{1}{3}}}$

Step 2

Move $b^{\frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$a^{\frac{5}{3}} b^{\frac{4}{3}} a^{\frac{4}{3}} b^{- \frac{1}{3}}$

Step 3

Multiply $a^{\frac{5}{3}}$ by $a^{\frac{4}{3}}$ by adding the exponents.

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Step 3.1

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

$a^{\frac{4}{3}} a^{\frac{5}{3}} b^{\frac{4}{3}} b^{- \frac{1}{3}}$

Step 3.2

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

$a^{\frac{4}{3} + \frac{5}{3}} b^{\frac{4}{3}} b^{- \frac{1}{3}}$

Step 3.3

Combine the numerators over the common denominator.

$a^{\frac{4 + 5}{3}} b^{\frac{4}{3}} b^{- \frac{1}{3}}$

Step 3.4

Add $4$ and $5$ .

$a^{\frac{9}{3}} b^{\frac{4}{3}} b^{- \frac{1}{3}}$

Step 3.5

Divide $9$ by $3$ .

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

Step 4

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

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Step 4.1

Move $b^{- \frac{1}{3}}$ .

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

Step 4.2

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

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

Step 4.3

Combine the numerators over the common denominator.

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

Step 4.4

Add $- 1$ and $4$ .

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

Step 4.5

Divide $3$ by $3$ .

$a^{3} b^{1}$

Step 5

Simplify $a^{3} b^{1}$ .

$a^{3} b$