Simplify:$ \frac{(25)^{3 / 2} \times(243)^{3 / 5}}{(16)^{5 / 4} \times(8)^{4 / 3}} $

Given:

\( \frac{(25)^{3 / 2} \times(243)^{3 / 5}}{(16)^{5 / 4} \times(8)^{4 / 3}} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$

Therefore,

$\frac{(25)^{3 / 2} \times(243)^{3 / 5}}{(16)^{5 / 4} \times(8)^{4 / 3}}=\frac{(5^{2})^{\frac{3}{2}} \times(3^{5})^{\frac{3}{5}}}{(2^{4})^{\frac{5}{4}} \times(2^{3})^{\frac{4}{3}}}$

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

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

$=\frac{125 \times 27}{32 \times 16}$

$=\frac{3375}{512}$

Hence, $\frac{(25)^{3 / 2} \times(243)^{3 / 5}}{(16)^{5 / 4} \times(8)^{4 / 3}}=\frac{3375}{512}$. 

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Updated on: 10-Oct-2022

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