Maths-
General
Easy
Question
Simplify:
(64 / 125)−2/3 ÷ (625 / 256)1/4 × (−6)0
Hint:
In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
an = a × a × ... × a n times.
The correct answer is: Simplifying the given expression, we get- 1.25 or 5/4.
Step-by-step solution:-
(64/125)−2/3 ÷ (625/256)1/4 × (−6)0
= (125/64)2/3 ÷ (625/256)1/4 × 1 ….......................................... (b-n = 1/bn & b0 = 1)
= (53/26)2/3 ÷ (54/28)1/4
= 53×2/3 / 26×2/3 ÷ (54×1/4 / 28×1/4) …........................................... [(bn)m = bnm]
= 52 / 24 ÷ 5 / 22
= 52 / 24 × 22 / 5 ................................................................... (Taking reciprocal)
= 52 × 22 / 24 × 5
= 52-1 / 24-2 ..................................................................................... (an/am = an-m)
= 5/22
= 5/4
= 1.25
Final Answer:-
∴ Simplifying the given expression, we get- 1.25 or 5/4.
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