Evaluate 5^0.25 × 125^0.25 / 256^0.10 × 256^0.15

The correct answer is: Simplifying the given expression, we get- 1.25 or 5/4.

Step-by-step solution:-
5^0.25 × 125^0.25 / 256^0.10 × 256^0.15
= (5×125)^0.25 / 256 ^(0.10+0.15) …......................................... [aⁿ × bⁿ = (ab)ⁿ & aⁿ × a^m = a^n+m]
= 625^0.25 / 256^0.25
= 625^1/4 / 256^1/4 …......................................................... (1/4 = 0.25)
= (5⁴)^1/4 / (4⁴)^1/4 ............................................................ [(bⁿ)^m = b^nm]
= 5 / 4
= 1.25
Final Answer:-
∴ Simplifying the given expression, we get- 1.25 or 5/4.