((5.1)^5/(5.1)^7)^3

asked by guest
on Jan 24, 2025 at 9:51 am



You asked:

Evaluate the expression: \({\left( \frac{{5.1}^{5}}{{5.1}^{7}} \right)}^{3}\)

MathBot Answer:

\[{\left( \frac{{5.1}^{5}}{{5.1}^{7}} \right)}^{3} = \frac{1000000}{17596287801} \approx 0.00005683016845991629163624407805\]

\[\begin{aligned}{\left( \frac{{5.1}^{5}}{{5.1}^{7}} \right)}^{3}& = \left(\left(5 + \frac{1}{10}\right)^{5} \cdot \frac{1}{\left(5 + \frac{1}{10}\right)^{7}}\right)^{3}\\& = \left(\left(\frac{51}{10}\right)^{5} \cdot \frac{1}{\left(5 + \frac{1}{10}\right)^{7}}\right)^{3}\\& = \left(\frac{345025251}{100000} \cdot \frac{1}{\left(5 + \frac{1}{10}\right)^{7}}\right)^{3}\\& = \left(\frac{345025251}{100000} \cdot \frac{1}{\left(\frac{51}{10}\right)^{7}}\right)^{3}\\& = \left(\frac{345025251}{100000} \cdot \frac{1}{\frac{897410677851}{10000000}}\right)^{3}\\& = \left(\frac{100}{2601}\right)^{3}\\& = \frac{1000000}{17596287801}\end{aligned}\]

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