Pre-Algebra Examples

$x^{- \frac{1}{3}} x^{- \frac{3}{5}}$

Step 1

Multiply $x^{- \frac{1}{3}}$ by $x^{- \frac{3}{5}}$ 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.

$x^{- \frac{1}{3} - \frac{3}{5}}$

Step 1.2

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x^{- \frac{1}{3} \cdot \frac{5}{5} - \frac{3}{5}}$

Step 1.3

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x^{- \frac{1}{3} \cdot \frac{5}{5} - \frac{3}{5} \cdot \frac{3}{3}}$

Step 1.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$x^{- \frac{5}{3 \cdot 5} - \frac{3}{5} \cdot \frac{3}{3}}$

Step 1.4.2

Multiply $3$ by $5$ .

$x^{- \frac{5}{15} - \frac{3}{5} \cdot \frac{3}{3}}$

Step 1.4.3

Multiply $\frac{3}{5}$ by $\frac{3}{3}$ .

$x^{- \frac{5}{15} - \frac{3 \cdot 3}{5 \cdot 3}}$

Step 1.4.4

Multiply $5$ by $3$ .

$x^{- \frac{5}{15} - \frac{3 \cdot 3}{15}}$

Step 1.5

Combine the numerators over the common denominator.

$x^{\frac{- 5 - 3 \cdot 3}{15}}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 3$ by $3$ .

$x^{\frac{- 5 - 9}{15}}$

Step 1.6.2

Subtract $9$ from $- 5$ .

$x^{\frac{- 14}{15}}$

Step 1.7

Move the negative in front of the fraction.

$x^{- \frac{14}{15}}$

Step 2

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

$\frac{1}{x^{\frac{14}{15}}}$