Simplify the Radical Expression x^-2*x^(11/9)

$x^{- 2} \cdot x^{\frac{11}{9}}$

Step 1

Multiply $x^{- 2}$ by $x^{\frac{11}{9}}$ by adding the exponents.

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

$x^{- 2 + \frac{11}{9}}$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$x^{- 2 \cdot \frac{9}{9} + \frac{11}{9}}$

Combine $- 2$ and $\frac{9}{9}$ .

$x^{\frac{- 2 \cdot 9}{9} + \frac{11}{9}}$

Combine the numerators over the common denominator.

$x^{\frac{- 2 \cdot 9 + 11}{9}}$

Simplify the numerator.

Multiply $- 2$ by $9$ .

$x^{\frac{- 18 + 11}{9}}$

Add $- 18$ and $11$ .

$x^{\frac{- 7}{9}}$

Move the negative in front of the fraction.

$x^{- \frac{7}{9}}$

Step 2

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

$\frac{1}{x^{\frac{7}{9}}}$