Find the simplified value of the given expression. {(2³× 8²)³÷ (4^{5}× 16²)}{(32²÷ 2^{4})²}

Correct Answer is : 2−32^{-3}2−3

Correct Answer is : 2−32^{-3}2−3

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RRB ALP CBT I 11 Feb 2026 Shift 1 Paper

Question : 58 of 75

Marks: +1, -0

\frac{(2^{3}\times 8^{2})^{3}\div (4^{5}\times 16^{2})}{(32^{2}\div 2^{4})^{2}}

Solution:

Concept:

Convert every base into

2

and then apply the laws of exponents.

Explanation:

Use the conversions:

8 = 2^3

4 = 2^2

16 = 2^4

, and

32 = 2^5

Simplify the numerator:

(2^3 \times (2^3)^2)^3 \div ((2^2)^5 \times (2^4)^2)

This becomes

(2^3 \times 2^6)^3 \div (2^{10} \times 2^8)

Using

(a^m)^n = a^{mn}

and

a^m \times a^n = a^{m+n}

, we get

(2^9)^3 \div 2^{18} = 2^{27} \div 2^{18} = 2^9

Simplify the denominator:

((2^5)^2 \div 2^4)^2 = (2^{10} \div 2^4)^2

Using

a^m \div a^n = a^{m-n}

, we get

(2^6)^2 = 2^{12}

Now divide the two results:

2^9 \div 2^{12} = 2^{9-12} = 2^{-3}

Answer:

The simplified value is

2^{-3}

, so the correct option is D.

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