Questions: Rewrite the expression with a positive rational exponent. (2xy)^(-5/7) Rewrite the expression. (2xy)^(-5/7)= (Use integers or fractions for any numbers in the expression)

$Rewrite the expression with a positive rational exponent. (2xy)^(-5/7) Rewrite the expression. (2xy)^(-5/7)= (Use integers or fractions for any numbers in the expression)$

Transcript text: Rewrite the expression with a positive rational exponent. \[ (2 x y)^{-\frac{5}{7}} \] Rewrite the expression. \[ (2 x y)^{-\frac{5}{7}}=\square \] (Use integers or fractions for any numbers in the expression)

Solution

Solution Steps

Step 1: Rewrite the expression with a positive exponent

To rewrite $(2xy)^{-\frac{5}{7}}$ with a positive exponent, use the property of exponents that states $a^{-b} = \frac{1}{a^b}$. Applying this property: \[ (2xy)^{-\frac{5}{7}} = \frac{1}{(2xy)^{\frac{5}{7}}} \]

Step 2: Express the denominator with a rational exponent

The expression $\frac{1}{(2xy)^{\frac{5}{7}}}$ is already in the desired form with a positive rational exponent. No further simplification is needed.

Step 3: Final rewritten expression

The final rewritten expression is: \[ (2xy)^{-\frac{5}{7}} = \frac{1}{(2xy)^{\frac{5}{7}}} \]