Question

simplify (2/5)whole power-3*(25/4)whole power-2​

Answer 1

Answer:

$\left(\frac{2}{5}\right)^{-3} \times \left(\frac{25}{4}\right)^{-2}=\frac{2}{5}$

Step-by-step explanation:

$\left(\frac{2}{5}\right)^{-3} \times \left(\frac{25}{4}\right)^{-2}$

$=\left(\frac{2}{5}\right)^{-3} \times \left(\frac{5^{2}}{2^{2}}\right)^{-2}$

$=\left(\frac{2}{5}\right)^{-3} \times [\left(\frac{5}{2}\right)^{2}]^{-2}$

$=\left(\frac{2}{5}\right)^{-3} \times \left(\frac{5}{2}\right)^{2\times -2}$

$=\left(\frac{2}{5}\right)^{-3} \times \left(\frac{5}{2}\right)^{-4}$

$=\left(\frac{2}{5}\right)^{-3} \times \left(\frac{2}{5}\right)^{4}$

$=\left(\frac{2}{5}\right)^{-3+4}$

$=\left(\frac{2}{5}\right)^{1}$

$=\frac{2}{5}$

Therefore,

$\left(\frac{2}{5}\right)^{-3} \times \left(\frac{25}{4}\right)^{-2}=\frac{2}{5}$

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Answer 2

Hey mate here is your answer.