MCQ
The value of $\{5(8^{\frac{1}{4}}+27^{\frac{1}{3}})^3\}^{\frac{1}{4}}$ is:
- A$27$
- B$8$
- ✓$5$
- D$1$
✓
Answer
Correct option: C.
$5$
$\{5(8^{\frac{1}{4}}+27^{\frac{1}{3}})^3\}^{\frac{1}{4}}$
$\Rightarrow\{5(2^{3\times\frac{1}{3}}+3^{3\times\frac{1}{3}})^3\}^{\frac{1}{4}}$
$\Rightarrow\{5(3+2)^3\}^{\frac{1}{4}}$
$\Rightarrow\{5\times5^3\}^{\frac{1}{4}}$
$\Rightarrow5^{4\times\frac{1}{4}}$
$\Rightarrow5$
$\Rightarrow\{5(2^{3\times\frac{1}{3}}+3^{3\times\frac{1}{3}})^3\}^{\frac{1}{4}}$
$\Rightarrow\{5(3+2)^3\}^{\frac{1}{4}}$
$\Rightarrow\{5\times5^3\}^{\frac{1}{4}}$
$\Rightarrow5^{4\times\frac{1}{4}}$
$\Rightarrow5$
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