Maths / Exponents and Power / Law 2 Division of Exponents

QUESTION

Find the value of the following: $\dpi{120} \fn_jvn \large (\frac{-3}{5})^4X(\frac{4}{9})^4X(\frac{-15}{18})^2$

 OPTIONS A. 64/125 B. 64/1825 C. 64/3125 D. 64/18225
Right Option : D

EXPLANATION
Explain TypeExplanation Content
Text

$\dpi{120} \fn_jvn \large (\frac{-3}{5})^4X(\frac{4}{9})^4X(\frac{-15}{18})^2$

$\dpi{120} \fn_jvn \large (\frac{-3}{5})^4X(\frac{2^2}{3^2})^4X(\frac{-3X5}{9X2})^2$

$\dpi{120} \fn_jvn \large (\frac{-3}{5})^4X(\frac{2}{3})^8X(\frac{-3^2X5^2}{3^4X2^2})$

$\dpi{120} \fn_jvn \large (\frac{3}{5})^4X(\frac{2}{3})^8X(\frac{3^2X5^2}{3^4X2^2})$  As Multiplication of two negative terms give positive

$\dpi{120} \fn_jvn \large (\frac{3^-^6}{5^4})X{2^8}X(\frac{5^2}{2^2})$

$\dpi{120} \fn_jvn \large {3^-^6}X{2^6}X{5^-^2}$

$\dpi{120} \fn_jvn \large \frac{2^6}{{3^6}\times{5^2}}$

$\dpi{120} \fn_jvn \large \dpi{120} \fn_jvn \large \frac{64}{729\times25}$

$\dpi{120} \fn_jvn \large \frac{64}{18225}$

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