Simplify x^-5x^(2/3)

$x^{- 5} x^{\frac{2}{3}}$

Step 1

Multiply $x^{- 5}$ by $x^{\frac{2}{3}}$ by adding the exponents.

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

$x^{- 5 + \frac{2}{3}}$

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

$x^{- 5 \cdot \frac{3}{3} + \frac{2}{3}}$

Combine $- 5$ and $\frac{3}{3}$ .

$x^{\frac{- 5 \cdot 3}{3} + \frac{2}{3}}$

Combine the numerators over the common denominator.

$x^{\frac{- 5 \cdot 3 + 2}{3}}$

Simplify the numerator.

Multiply $- 5$ by $3$ .

$x^{\frac{- 15 + 2}{3}}$

Add $- 15$ and $2$ .

$x^{\frac{- 13}{3}}$

Move the negative in front of the fraction.

$x^{- \frac{13}{3}}$

Step 2

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

$\frac{1}{x^{\frac{13}{3}}}$