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((1)/(3))^(-2)÷((3)/(5))^(-3)

$\left(\frac{1}{3}\right)^{-2} \div\left(\frac{3}{5}\right)^{-3}$

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Multiplication with rational exponents

Full solution

Q.

\left(\frac{1}{3}\right)^{-2} \div\left(\frac{3}{5}\right)^{-3}

Convert to Positive Exponents: Step $1$ : Convert the negative exponents to positive by taking the reciprocal of the bases. $\newline$ Calculation: $\left(\frac{1}{3}\right)^{-2}$ becomes $\left(\frac{3}{1}\right)^2$ and $\left(\frac{3}{5}\right)^{-3}$ becomes $\left(\frac{5}{3}\right)^3$ .
Calculate Powers: Step $2$ : Calculate the powers. $\newline$ Calculation: $(\frac{3}{1})^2 = 9$ and $(\frac{5}{3})^3 = \frac{125}{27}$ .
Perform Division: Step $3$ : Perform the division of the results from Step $2$ . $\newline$ Calculation: $9 \div (125/27) = 9 \times (27/125) = 243/125$ .

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