Simplify:

\(\rm \left((4^4)^2\times \frac{1}{64^2}\right)^2+10=?\)

Question

Question

This question was previously asked in

RPF SI (2018) Official Paper (Held On: 19 Dec, 2018 Shift 1)

Answer 1

Given:

Simplify: ((4⁴)² × (1)/(64²))² + 10

Concept:

Exponentiation rules and simplification

Formula Used:

(a^m)ⁿ = a^m×n

a^m / aⁿ = a^m-n

Calculation:

We have,

⇒ ((4⁴)² × (1)/(64²))² + 10

First, simplify inside the parentheses:

⇒ (4^4×2 × (1)/(64²))² + 10

⇒ (4⁸ × (1)/(64²))² + 10

Since 64 = 4³, we can write:

⇒ (4⁸ × 1/(4^3×2))² + 10

⇒ (4⁸ × 1/(4⁶))² + 10

⇒ (4^8-6)² + 10

⇒ (4²)² + 10

⇒ 4^2×2 + 10

⇒ 4⁴ + 10

Calculate 4⁴:

⇒ 256 + 10

⇒ 266

∴ The correct answer is option 4.

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