Quantitative Aptitude – Indices and Surds

Slot – 1 – Quantitative Aptitude – Indices and Surds – if m and n are integers such that

Q. If m and n are integers such that (√2)^19 3^4 4^2 9^m 8^n = 3^n 16^m (4√64) then m is?

1. -20
2. -24
3. -16
4. -12

Answer: -12

Solution: Given, √2^19 3^4 4^2 9^m 8^n=3^n 16^m ∜64
Or 2^(19/2)×3^4×2^4×3^2m×2^3n= 3^n×2^4m×2^(6/4)
2^(19/2+4+3n)×3^(4+2m)=3^n×2^((4m+6/4) )
Comparing both sides,
n = 4+2m
19/2 +4 + 3n = 4m + 6/4
Or (19 + 8)/2 + 3(4+2m) = 4m + 3/2
27/2 + 12 + 6m = 4m + 3/2
6m -4m = 3/2 – 27/2 -12
2m = -24
Thus m = -12

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