Question

Evaluate the following:
(24/5)to the power -4(/12/15)to the power 6 *(6/4) to the power 5

Answer 1

$\textbf{Given:}$

$\mathsf{\left(\dfrac{24}{5}\right)^{-4}{\times}\left(\dfrac{12}{15}\right)^6{\times}\left(\dfrac{6}{4}\right)^5}$

$\textbf{To simplify:}$

$\mathsf{\left(\dfrac{24}{5}\right)^{-4}{\times}\left(\dfrac{12}{15}\right)^6{\times}\left(\dfrac{6}{4}\right)^5}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\left(\dfrac{24}{5}\right)^{-4}{\times}\left(\dfrac{12}{15}\right)^6{\times}\left(\dfrac{6}{4}\right)^5}$

$\mathsf{=\left(\dfrac{5}{24}\right)^{4}{\times}\left(\dfrac{4}{5}\right)^6{\times}\left(\dfrac{3}{2}\right)^5}$

$\mathsf{=\left(\dfrac{5}{4{\times}6}\right)^{4}{\times}\left(\dfrac{4}{5}\right)^6{\times}\left(\dfrac{3}{2}\right)^5}$

$\mathsf{=\dfrac{5^4}{4^4{\times}6^4}{\times}\dfrac{4^6}{5^6}{\times}\dfrac{3^5}{2^5}}$

$\mathsf{=\dfrac{1}{6^4}{\times}\dfrac{4^2}{5^2}{\times}\dfrac{3^5}{2^5}}$

$\mathsf{=\dfrac{1}{2^4{\times}3^4}{\times}\dfrac{2^4}{5^2}{\times}\dfrac{3^5}{2^5}}$

$\mathsf{=\dfrac{1}{5^2}{\times}\dfrac{3}{2^5}}$

$\mathsf{=\dfrac{3}{800}}$

$\implies\boxed{\mathsf{\left(\dfrac{24}{5}\right)^{-4}{\times}\left(\dfrac{12}{15}\right)^6{\times}\left(\dfrac{6}{4}\right)^5=\dfrac{3}{800}}}$

$\textbf{Find more:}$

6⁶+6⁶+6⁶+6⁶+6⁶+6⁶+6⁶+6⁶+6⁶/2⁶+2⁶×5⁶+5⁶+5⁶+5⁶/3⁶+3⁶+3⁶​

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