Pre-Algebra Examples

$x^{- \frac{3}{2}} \div x^{- \frac{3}{4}}$

Step 1

Rewrite the division as a fraction.

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

Step 2

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

$\frac{1}{x^{- \frac{3}{4}} x^{\frac{3}{2}}}$

Step 3

Multiply $x^{- \frac{3}{4}}$ by $x^{\frac{3}{2}}$ 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.

$\frac{1}{x^{- \frac{3}{4} + \frac{3}{2}}}$

Step 3.2

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

$\frac{1}{x^{- \frac{3}{4} + \frac{3}{2} \cdot \frac{2}{2}}}$

Step 3.3

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

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Step 3.3.1

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

$\frac{1}{x^{- \frac{3}{4} + \frac{3 \cdot 2}{2 \cdot 2}}}$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{1}{x^{- \frac{3}{4} + \frac{3 \cdot 2}{4}}}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{1}{x^{\frac{- 3 + 3 \cdot 2}{4}}}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $3$ by $2$ .

$\frac{1}{x^{\frac{- 3 + 6}{4}}}$

Step 3.5.2

Add $- 3$ and $6$ .

$\frac{1}{x^{\frac{3}{4}}}$