Simplify x^(2/9)*x^(-4/9)

$x^{\frac{2}{9}} \cdot x^{- \frac{4}{9}}$

Step 1

Multiply $x^{\frac{2}{9}}$ by $x^{- \frac{4}{9}}$ by adding the exponents.

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

$x^{\frac{2}{9} - \frac{4}{9}}$

Combine the numerators over the common denominator.

$x^{\frac{2 - 4}{9}}$

Subtract $4$ from $2$ .

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

Move the negative in front of the fraction.

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

Step 2

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

$\frac{1}{x^{\frac{2}{9}}}$