Maths / Exponents and Power / Law 2 Division of Exponents

QUESTION

Evaluate the following:

• $\dpi{120} \fn_jvn \large \\ (\frac{-3}{4})^4\times (\frac{125}{27})/(\frac{5}{2})^2\times \frac{9}{16}\\\\$
• $\dpi{120} \fn_jvn \large (\frac{-2}{3})^4\times (\frac{216}{125})/(\frac{6}{5})^2\times \frac{4}{9}$
• EXPLANATION
Explain TypeExplanation Content
Text

$\\ a) \;(\frac{-3}{4})^4\times (\frac{125}{27})/(\frac{5}{2})^2\times \frac{9}{16}\\\\ =(\frac{-3}{4})^4\times (\frac{5}{3})^3/(\frac{5}{2})^2\times (\frac{3}{4})^2\\\\ =(\frac{-3}{4})^4\times (\frac{5}{3})^3/(\frac{5\times 3}{2\times 4})^2\\\\ =(\frac{-3}{4})^4\times (\frac{5}{3})^3/(\frac{15}{8})^2 \\\\ b)\;(\frac{-2}{3})^4\times (\frac{216}{125})/(\frac{6}{5})^2\times \frac{4}{9}\\\\ =(\frac{-2}{3})^4\times (\frac{6}{5})^3/(\frac{6}{5})^2\times (\frac{2}{3})^2\\\\ =(\frac{-2}{3})^4\times (\frac{6}{5})^3/(\frac{6\times 2}{5\times 3})^2\\\\ =(\frac{-2}{3})^4\times (\frac{6}{5})^3/(\frac{12}{15})^2$

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