\sqrt{\frac{10^2-2^6}{\frac{3^3-2^3}{2^2}}}-\left(-\frac{3}{7}\right)^2\left(-\frac{3}{7}\right)^{-3}\left(\frac{7}{3}\right)^{-2}

asked by guest
on Nov 25, 2024 at 6:44 pm



You asked:

Evaluate the expression: 10226332322((37))2((37))3(73)2\sqrt{\frac{{10}^{2} - {2}^{6}}{\frac{{3}^{3} - {2}^{3}}{{2}^{2}}}} - {\left( -\left( \frac{3}{7} \right) \right)}^{2} {\left( -\left( \frac{3}{7} \right) \right)}^{-3} {\left( \frac{7}{3} \right)}^{-2}

MathBot Answer:

10226332322((37))2((37))3(73)2=37+1219193.18156023501816976231508636574592\sqrt{\frac{{10}^{2} - {2}^{6}}{\frac{{3}^{3} - {2}^{3}}{{2}^{2}}}} - {\left( -\left( \frac{3}{7} \right) \right)}^{2} {\left( -\left( \frac{3}{7} \right) \right)}^{-3} {\left( \frac{7}{3} \right)}^{-2} = \frac{3}{7} + \frac{12 \sqrt{19}}{19} \approx 3.18156023501816976231508636574592


10226332322((37))2((37))3(73)2=(10226)1(3323)122(37)21(37)31(73)2=(10026)1(3323)122(37)21(37)31(73)2=(10064)1(3323)122(37)21(37)31(73)2=361(3323)122(37)21(37)31(73)2=361(2723)122(37)21(37)31(73)2=361(278)122(37)21(37)31(73)2=36119122(37)21(37)31(73)2=361194(37)21(37)31(73)2=14419(37)21(37)31(73)2=121919(37)21(37)31(73)2=1219199491(37)31(73)2=121919949343271(73)2=12191994934327949=12191973949=12191937=121919+37=37+121919\begin{aligned}\sqrt{\frac{{10}^{2} - {2}^{6}}{\frac{{3}^{3} - {2}^{3}}{{2}^{2}}}} - {\left( -\left( \frac{3}{7} \right) \right)}^{2} {\left( -\left( \frac{3}{7} \right) \right)}^{-3} {\left( \frac{7}{3} \right)}^{-2}&=\sqrt{\left(10^{2} - 2^{6}\right) \cdot \frac{1}{\left(3^{3} - 2^{3}\right) \cdot \frac{1}{2^{2}}}} - \left(- \frac{3}{7}\right)^{2} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\sqrt{\left(100 - 2^{6}\right) \cdot \frac{1}{\left(3^{3} - 2^{3}\right) \cdot \frac{1}{2^{2}}}} - \left(- \frac{3}{7}\right)^{2} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\sqrt{\left(100 - 64\right) \cdot \frac{1}{\left(3^{3} - 2^{3}\right) \cdot \frac{1}{2^{2}}}} - \left(- \frac{3}{7}\right)^{2} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\sqrt{36 \cdot \frac{1}{\left(3^{3} - 2^{3}\right) \cdot \frac{1}{2^{2}}}} - \left(- \frac{3}{7}\right)^{2} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\sqrt{36 \cdot \frac{1}{\left(27 - 2^{3}\right) \cdot \frac{1}{2^{2}}}} - \left(- \frac{3}{7}\right)^{2} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\sqrt{36 \cdot \frac{1}{\left(27 - 8\right) \cdot \frac{1}{2^{2}}}} - \left(- \frac{3}{7}\right)^{2} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\sqrt{36 \cdot \frac{1}{19 \cdot \frac{1}{2^{2}}}} - \left(- \frac{3}{7}\right)^{2} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\sqrt{36 \cdot \frac{1}{\frac{19}{4}}} - \left(- \frac{3}{7}\right)^{2} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\sqrt{\frac{144}{19}} - \left(- \frac{3}{7}\right)^{2} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\frac{12}{19} \cdot \sqrt{19} - \left(- \frac{3}{7}\right)^{2} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\frac{12}{19} \cdot \sqrt{19} - \frac{9}{49} \cdot \frac{1}{\left(- \frac{3}{7}\right)^{3}} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\frac{12}{19} \cdot \sqrt{19} - \frac{9}{49} \cdot - \frac{343}{27} \cdot \frac{1}{\left(\frac{7}{3}\right)^{2}}\\&=\frac{12}{19} \cdot \sqrt{19} - \frac{9}{49} \cdot - \frac{343}{27} \cdot \frac{9}{49}\\&=\frac{12}{19} \cdot \sqrt{19} - - \frac{7}{3} \cdot \frac{9}{49}\\&=\frac{12}{19} \cdot \sqrt{19} - - \frac{3}{7}\\&=\frac{12}{19} \cdot \sqrt{19} + \frac{3}{7}\\&=\frac{3}{7} + \frac{12}{19} \cdot \sqrt{19}\end{aligned}