(7^-3/7^-5)^-2

asked by guest
on Jan 24, 2025 at 9:15 am



You asked:

Evaluate the expression: \({\left( \frac{{7}^{-3}}{{7}^{-5}} \right)}^{-2}\)

MathBot Answer:

\[{\left( \frac{{7}^{-3}}{{7}^{-5}} \right)}^{-2} = \frac{1}{2401} \approx 0.00041649312786339025406080799667\]

\[\begin{aligned}{\left( \frac{{7}^{-3}}{{7}^{-5}} \right)}^{-2}& = \frac{1}{\left(\frac{1}{7^{3}} \cdot \frac{1}{\frac{1}{7^{5}}}\right)^{2}}\\& = \frac{1}{\left(\frac{1}{343} \cdot \frac{1}{\frac{1}{7^{5}}}\right)^{2}}\\& = \frac{1}{\left(\frac{1}{343} \cdot \frac{1}{\frac{1}{16807}}\right)^{2}}\\& = \frac{1}{49^{2}}\\& = \frac{1}{2401}\end{aligned}\]

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