MCQ
The value of $\left\{9\left(64^{1 / 3}+125^{1 / 3}\right)^3\right\}^{1 / 4}$ is
- A3
- ✓9
- C$3 \sqrt{3}$
- D81
✓
Answer
Correct option: B.
9
(b)
$\left\{9\left(64^{1 / 3}+125^{1 / 3}\right)^3\right\}^{1 / 4}=\left[9\left\{\left(4^3\right)^{1 / 3}+\left(5^3\right)^{1 / 3}\right\}^3\right]^{1 / 4}$
$=\left(9(4+5)^3\right]^{1 / 4}=\left(9 \times 9^3\right)^{1 / 4}=\left(9^4\right)^{1 / 4}=9^{4 \times 1 / 4}=9^1=9$
$\left\{9\left(64^{1 / 3}+125^{1 / 3}\right)^3\right\}^{1 / 4}=\left[9\left\{\left(4^3\right)^{1 / 3}+\left(5^3\right)^{1 / 3}\right\}^3\right]^{1 / 4}$
$=\left(9(4+5)^3\right]^{1 / 4}=\left(9 \times 9^3\right)^{1 / 4}=\left(9^4\right)^{1 / 4}=9^{4 \times 1 / 4}=9^1=9$
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