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Question Number 187877 by nadovic last updated on 23/Feb/23

$$\mathrm{Simplify}\mathrm{completely}$$$$\frac{{256}^{-\frac{7}{16}}\times {128}^{\frac{9}{28}}}{{512}^{\frac{17}{36}}\times {64}^{-\frac{11}{12}}}$$

Answered by Rasheed.Sindhi last updated on 23/Feb/23

$$\frac{{256}^{-\frac{7}{16}}\times {128}^{\frac{9}{28}}}{{512}^{\frac{17}{36}}\times {64}^{-\frac{11}{12}}}$$$$=\frac{{256}^{\frac{1}{8}\cdot \frac{-7}{2}}\times {128}^{\frac{1}{7}\cdot \frac{9}{4}}}{{512}^{\frac{1}{9}\cdot \frac{17}{4}}\times {64}^{\frac{1}{6}\cdot \frac{-11}{2}}}$$$$=\frac{2^{-7/2}\times 2^{9/4}}{2^{17/4}\times 2^{-11/2}}$$$$=\frac{2^{-\frac{7}{2}+\frac{9}{4}}}{2^{\frac{17}{4}-\frac{11}{2}}}=\frac{2^{-\frac{5}{4}}}{2^{-\frac{5}{4}}}=2^{-\frac{5}{4}+\frac{5}{4}}=2^0=1$$

Commented by nadovic last updated on 23/Feb/23

$$Wow..ThankyouSir$$

Answered by HeferH last updated on 23/Feb/23

$$\frac{{\left(2^8\right)}^{-\frac{7}{16}}\cdot {\left(2^7\right)}^{\frac{9}{28}}}{{\left(2^9\right)}^{\frac{17}{36}}\cdot {\left(2^6\right)}^{-\frac{11}{12}}}=\frac{2^{-\frac{7}{2}}\cdot 2^{\frac{9}{4}}}{2^{\frac{17}{4}}\cdot 2^{-\frac{11}{2}}}=\frac{2^{\frac{9}{4}-\frac{7}{2}}}{2^{\frac{17}{4}-\frac{11}{2}}}=\frac{2^{-\frac{5}{4}}}{2^{-\frac{5}{4}}}=1$$

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