ABC26GN1875 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
Find the value of $\left\{(16)^{\frac{3}{2}}+(16)^{-\frac{3}{2}}\right\}$.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
$\left[(16)^{\frac{3}{2}}+(16)^{-\frac{3}{2}}\right]=\left[\left(4^{2}\right)^{\frac{3}{2}}+\left(4^{2}\right)^{-\frac{3}{2}}\right]=4^{\left(2 \times \frac{3}{2}\right)}+4^{\left\{2 \times \frac{(-3)}{2}\right\}}=4^{3}+4^{-3}=4^{3}+\frac{1}{4^{3}}=\left(64+\frac{1}{64}\right)=\frac{4097}{64}.$
Explanation as extracted from the printed page; notation may be imperfect.
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