Question

25raised3/2 into 243raised 2/5/ 16raised5/4 into 8raised4/3

Answer 1

Answer:

$\huge\boxed{\fcolorbox{red}{pink}{Your's Answer}}$

According to question:-

$\frac{ {25}^{ \frac{3}{2} } \times {243}^{ \frac{2}{5} } }{ {16}^{ \frac{5}{4} } \times {8}^{ \frac{4}{3} } }$

$= \frac{ {5}^{2 \times \frac{3}{2} } \times {3}^{5 \times \frac{2}{5} } }{ {2}^{4 \times \frac{5}{4} } \times {2}^{3 \times \frac{4}{3} } }$

$= \frac{5 \times 3}{2 \times 2}$

$= \frac{15}{4} \: or \: 3.75$

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Answer 2

Answer:

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:Question :}}$

$:\implies\sf \dfrac{(25)^{\Large\frac{3}{2}}\times(243)^{\Large\frac{2}{5}}}{(16)^{\Large\frac{5}{4}}\times(8)^{\Large\frac{4}{3}}}\\\\\\:\implies\sf \dfrac{(5)^{\bigg[{\Large2\times \frac{3}{2}}\bigg]}\times(3)^{\bigg[{\Large5 \times \frac{2}{5}}\bigg]}}{(2)^{\bigg[{\Large4 \times \frac{5}{4}}\bigg]}\times(2)^{\bigg[{\Large3 \times \frac{4}{3}}\bigg]}}\\\\\\:\implies\sf \dfrac{(5)^3 \times (3)^2}{(2)^5 \times (2)^4}\\\\\\:\implies\sf \dfrac{125 \times 9}{32 \times 16}\\\\\\:\implies\sf \dfrac{125 \times 9}{16 \times 2 \times 16}\\\\\\:\implies\sf \dfrac{125 \times (10 - 1)}{16^2 \times 2}\\\\\\:\implies\sf \dfrac{1250 - 125}{256 \times 2}\\\\\\:\implies\large\underline{\boxed{\sf \dfrac{1125}{512}}}$

$\rule{150}{2}$

$\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}$