Basic Math Examples

$\frac{b^{\frac{3}{4}}}{b^{- \frac{3}{2}}}$

Step 1

Move $b^{- \frac{3}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$b^{\frac{3}{4}} b^{\frac{3}{2}}$

Step 2

Multiply $b^{\frac{3}{4}}$ by $b^{\frac{3}{2}}$ by adding the exponents.

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Step 2.1

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

$b^{\frac{3}{4} + \frac{3}{2}}$

Step 2.2

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b^{\frac{3}{4} + \frac{3}{2} \cdot \frac{2}{2}}$

Step 2.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

$b^{\frac{3}{4} + \frac{3 \cdot 2}{2 \cdot 2}}$

Step 2.3.2

Multiply $2$ by $2$ .

$b^{\frac{3}{4} + \frac{3 \cdot 2}{4}}$

Step 2.4

Combine the numerators over the common denominator.

$b^{\frac{3 + 3 \cdot 2}{4}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3$ by $2$ .

$b^{\frac{3 + 6}{4}}$

Step 2.5.2

Add $3$ and $6$ .

$b^{\frac{9}{4}}$