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

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



You asked:

Evaluate the expression: (5.155.17)3{\left( \frac{{5.1}^{5}}{{5.1}^{7}} \right)}^{3}

MathBot Answer:

(5.155.17)3=100000017596287801≈0.00005683016845991629163624407805{\left( \frac{{5.1}^{5}}{{5.1}^{7}} \right)}^{3} = \frac{1000000}{17596287801} \approx 0.00005683016845991629163624407805

(5.155.17)3=((5110)55.17)3=(3450252511000005.17)3=(345025251100000(5110)7)3=(34502525110000089741067785110000000)3=(1002601)3=100000017596287801\begin{aligned}{\left( \frac{{5.1}^{5}}{{5.1}^{7}} \right)}^{3}&={\left( \frac{{\left( \frac{51}{10} \right)}^{5}}{{5.1}^{7}} \right)}^{3}\\&={\left( \frac{\frac{345025251}{100000}}{{5.1}^{7}} \right)}^{3}\\&={\left( \frac{\frac{345025251}{100000}}{{\left( \frac{51}{10} \right)}^{7}} \right)}^{3}\\&={\left( \frac{\frac{345025251}{100000}}{\frac{897410677851}{10000000}} \right)}^{3}\\&={\left( \frac{100}{2601} \right)}^{3}\\&=\frac{1000000}{17596287801}\end{aligned}

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