Finite Math Examples

$(b^{\frac{1}{4}} c^{- \frac{1}{3}}) (b^{\frac{3}{4}} c^{- \frac{5}{3}})$

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Add $3$ and $1$ .

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

Step 1.5

Divide $4$ by $4$ .

$b^{1} c^{- \frac{1}{3}} c^{- \frac{5}{3}}$

Step 2

Simplify $b^{1} c^{- \frac{1}{3}} c^{- \frac{5}{3}}$ .

$b c^{- \frac{1}{3}} c^{- \frac{5}{3}}$

Step 3

Multiply $c^{- \frac{1}{3}}$ by $c^{- \frac{5}{3}}$ by adding the exponents.

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Step 3.1

Move $c^{- \frac{5}{3}}$ .

$b (c^{- \frac{5}{3}} c^{- \frac{1}{3}})$

Step 3.2

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

$b c^{- \frac{5}{3} - \frac{1}{3}}$

Step 3.3

Combine the numerators over the common denominator.

$b c^{\frac{- 5 - 1}{3}}$

Step 3.4

Subtract $1$ from $- 5$ .

$b c^{\frac{- 6}{3}}$

Step 3.5

Divide $- 6$ by $3$ .

$b c^{- 2}$

Step 4

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

$b \frac{1}{c^{2}}$

Step 5

Combine $b$ and $\frac{1}{c^{2}}$ .

$\frac{b}{c^{2}}$