Solve: 16³/2}+16^{-3/2}=?

Correct Answer is : 4097644097/64644097

Correct Answer is : 4097644097/64644097

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SSC CHSL 13 Nov 2025 Shift 3 Paper

Question : 74 of 100

Marks: +1, -0

Solve:

16^{3/2}+16^{-3/2}=?

Solution:

Concept:

Use exponent rules:

a^{m/n} = (a^{1/n})^m

and

a^{-n} = \frac{1}{a^n}

. Convert fractional and negative exponents to simpler forms.

Explanation:

Compute

16^{3/2}

first. Since

16^{1/2} = 4

, then

16^{3/2} = (16^{1/2})^3 = 4^3 = 64

Next,

16^{-3/2} = \frac{1}{16^{3/2}} = \frac{1}{64}

(using the negative exponent rule).

Add the two results:

64 + \frac{1}{64} = \frac{64 \times 64}{64} + \frac{1}{64} = \frac{4096}{64} + \frac{1}{64} = \frac{4097}{64}

Answer:

\frac{4097}{64}

which matches option A.

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