Basic Math Examples

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

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

Step 1

Move

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

$a^{- \frac{4}{3}}$ to the numerator using the negative exponent rule

\frac{1}{b^{- n}} = b^{n}

$\frac{1}{b^{- n}} = b^{n}$ .

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

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

Step 2

Move

b^{\frac{1}{3}}

$b^{\frac{1}{3}}$ to the numerator using the negative exponent rule

\frac{1}{b^{n}} = b^{- n}

$\frac{1}{b^{n}} = b^{- n}$ .

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

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

Step 3

Multiply

a^{\frac{5}{3}}

$a^{\frac{5}{3}}$ by

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

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

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Step 3.1

Move

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

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

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

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

$a^{3} b$