MCQ
If $64^{-\frac{1}{3}}\Big(64^{\frac{1}{3}}-64^\frac{2}{3}\Big)$ then $5\sqrt[\text{n}]{64}=$
- A$25$
- B$\frac{1}{125}$
- C$625$
- D$\frac{1}{5}$
✓
Answer
- $25$
Solution:
We have to find $5\sqrt[\text{n}]{64}$ provided $\sqrt{5^\text{n}}=125$
So,
$\sqrt{5^\text{n}}=125$
$5^{\text{n}\times\frac{1}{2}}=5^3$
$\frac{\text{n}}{2}=3$
$\text{n}=3\times2$
$\text{n}=6$
Substitute $\text{n}=6$ in $5^{\sqrt[\text{n}]{64}}$ to get
$5^{\sqrt[\text{n}]{64}}=5^{2^{6\times\frac{1}{6}}}$
$=5\times5$
$=25$
Hence the value of $5^{\sqrt[\text{n}]{64}}$ is 25
The correct choice is a.
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