Question

Evaluate (81/16)^-3/4 × ((9/25)^3/2 ÷ (5/2)^-3)

Answer 1

fully answer, with Evaluate

Answer 2

Answer:

$\left(\frac{81}{16}\right)^{\frac{-3}{4}}\times [\left(\frac{9}{25}\right)^{\frac{3}{2}}\div \left(\frac{5}{2}\right)^{-3}]=1$

Step-by-step explanation:

$\left(\frac{81}{16}\right)^{\frac{-3}{4}}\times [\left(\frac{9}{25}\right)^{\frac{3}{2}}\div \left(\frac{5}{2}\right)^{-3}]$

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

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

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

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

$=1^{3}$

Therefore,

$\left(\frac{81}{16}\right)^{\frac{-3}{4}}\times [\left(\frac{9}{25}\right)^{\frac{3}{2}}\div \left(\frac{5}{2}\right)^{-3}]=1$

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