MCQ
The value of $(\frac{81}{16})^{\frac{-3}{4}}\times\{(\frac{25}{9})^{\frac{-3}{2}}\div(\frac{5}{2})^{-3}\}$ is:
- A2
- B3
- C1
- D4
✓
Answer
- 1
Solution:
$(\frac{81}{16})^{\frac{-3}{4}}\times\{(\frac{25}{9})^{\frac{-3}{2}}\div(\frac{5}{2})^{-3}\}$
$\Rightarrow(\frac{3}{2})^{4\times\frac{-3}{4}}\times\{(\frac{5}{3})^{2\times\frac{-3}{2}}\div(\frac{5}{2})^{-3}\}$
$\Rightarrow(\frac{3}{2})^{-3}\times\{(\frac{5}{3})^{-3}\div(\frac{5}{2})^{-3}\}$
$\Rightarrow(\frac{3}{2})^{-3}\times(\frac{5}{3}\times\frac{2}{5})^{-3}$
$\Rightarrow(\frac{3}{2})^{-3}\times(\frac{2}{3})^{-3}$
$\Rightarrow(\frac{3}{2}\times\frac{2}{3})^{-3}$
$\Rightarrow(1)^{-3}=1$
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