Simplify:
(1/4)⁻² − 3 (8)^2/3 (4⁰) + (9/16)^−1/2

The correct answer is: Simplifying the given expression, we get- 16/3 or 5.33.

Step-by-step solution:-
(1/4)⁻² − 3 (8)^2/3 (4⁰) + (9/16)^−1/2
= (4)² − 3 (8)^2/3 × 1 + (16/9)^1/2…........................................................................... (b^-n = 1/bⁿ & b⁰ = 1)
= (2²)² - 3 (2³)^2/3 + (2⁴/3²)^1/2
= 2⁴ - 3 × 2² + 2^4×1/2 / 3^2×1/2 ............................................................................. [(bⁿ)^m = b^nm]
= 2⁴ - 3 × 2² + 2² / 3
= 16 - 3×4 + 4/3
= 16 - 12 +4/3
= 4 + 4/3
= 12/3 + 4/3
= 12+4 / 3
= 16/3 = 5.33
Final Answer:-
∴ Simplifying the given expression, we get- 16/3 or 5.33.