Algebra Examples

$\frac{a^{\frac{3}{4}} b^{- 1} \cdot b^{\frac{7}{4}}}{3 b^{- 1}}$

Step 1

Multiply $b^{- 1}$ by $b^{\frac{7}{4}}$ by adding the exponents.

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Step 1.1

Move $b^{\frac{7}{4}}$ .

$\frac{a^{\frac{3}{4}} (b^{\frac{7}{4}} b^{- 1})}{3 b^{- 1}}$

Step 1.2

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

$\frac{a^{\frac{3}{4}} b^{\frac{7}{4} - 1}}{3 b^{- 1}}$

Step 1.3

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{a^{\frac{3}{4}} b^{\frac{7}{4} - 1 \cdot \frac{4}{4}}}{3 b^{- 1}}$

Step 1.4

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

$\frac{a^{\frac{3}{4}} b^{\frac{7}{4} + \frac{- 1 \cdot 4}{4}}}{3 b^{- 1}}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{a^{\frac{3}{4}} b^{\frac{7 - 1 \cdot 4}{4}}}{3 b^{- 1}}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 1$ by $4$ .

$\frac{a^{\frac{3}{4}} b^{\frac{7 - 4}{4}}}{3 b^{- 1}}$

Step 1.6.2

Subtract $4$ from $7$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

Move $b$ .

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

Step 3.2

Multiply $b$ by $b^{\frac{3}{4}}$ .

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Step 3.2.1

Raise $b$ to the power of $1$ .

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

Step 3.2.2

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

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

Step 3.3

Write $1$ as a fraction with a common denominator.

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Add $4$ and $3$ .

$\frac{a^{\frac{3}{4}} b^{\frac{7}{4}}}{3}$