Maths-
General
Easy
Question
Compute [(64)−1/6 × (216)−1/3 × (81)1/4 ] / [(512)−1/3 × (16)1/4 × (9)−1/2]
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: Value after simplifying the given equation is 3.
Step-by-step solution:-
[(64)−1/6 × (216)−1/3 × (81)1/4] / [(512)−1/3 × (16)1/4 × (9)−1/2]
= [(81)1/4 × (512)1/3 × (9)1/2] / [(64)1/6 × (216)1/3 × (16)1/4] ...................................... (b-n = 1/bn)
= [(34)1/4 × (83)1/3 × (32)1/2] / [(26)1/6 × (63)1/3 × (24)1/4]
= [31 × 81 × 31] / [21 × 61 × 21] .................................................................................. [(bn)m = bnm]
= 3 × 8 × 3 / 2 × 6 × 2
= 72 / 24
= 3
Final Answer:-
∴ Value after simplifying the given equation is 3.
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