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((3)/(x))^(2)×((3)/(x))^(-1)

$\left(\frac{3}{x}\right)^{2} \times\left(\frac{3}{x}\right)^{-1}$

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Evaluate rational exponents

Full solution

Q.

\left(\frac{3}{x}\right)^{2} \times\left(\frac{3}{x}\right)^{-1}

Identify Bases and Exponents: Identify the bases and exponents in the expression. $\newline$ $((3)/(x))^2$ has a base of $(3/x)$ and an exponent of $2$ . $\newline$ $((3)/(x))^(-1)$ has the same base $(3/x)$ and an exponent of $-1$ .
Combine Terms Using Property: Use the property of exponents that states $(a^m)\times(a^n) = a^{(m+n)}$ to combine the terms. $\newline$ $\left(\frac{3}{x}\right)^2 \times \left(\frac{3}{x}\right)^{-1} = \left(\frac{3}{x}\right)^{2 + (-1)}$
Add Exponents: Add the exponents. $\newline$ $2 + (-1) = 1$ $\newline$ So, $\left(\frac{3}{x}\right)^{2 + (-1)} = \left(\frac{3}{x}\right)^1$
Simplify Expression: Simplify the expression. $\left(\frac{3}{x}\right)^1 = \frac{3}{x}$

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