Precalculus Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Add $5$ and $3$ .

$\frac{b^{\frac{8}{4}}}{b^{\frac{1}{4}}}$

Step 1.4

Divide $8$ by $4$ .

$\frac{b^{2}}{b^{\frac{1}{4}}}$

Step 2

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

$b^{2} b^{- \frac{1}{4}}$

Step 3

Multiply $b^{2}$ by $b^{- \frac{1}{4}}$ 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.

$b^{2 - \frac{1}{4}}$

Step 3.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$b^{2 \cdot \frac{4}{4} - \frac{1}{4}}$

Step 3.3

Combine $2$ and $\frac{4}{4}$ .

$b^{\frac{2 \cdot 4}{4} - \frac{1}{4}}$

Step 3.4

Combine the numerators over the common denominator.

$b^{\frac{2 \cdot 4 - 1}{4}}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $4$ .

$b^{\frac{8 - 1}{4}}$

Step 3.5.2

Subtract $1$ from $8$ .

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