Maths-
General
Easy
Question
Evaluate 1 / (216)−2/3 + 1 / (256)−3/4 + 1 / (32)−1/5
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: The given expression when simplified, gives the value 102.
Step-by-step solution:-
1 / (216)−2/3 + 1 / (256)−3/4 + 1 / (32)−1/5
= (1/216)-2/3 + (1/256)-3/4 + (1/32)-1/5 …........................................................................... (1n = 1)
= 2162/3 + 2563/4 + 321/5 …................................................................................................ (b-n = 1/bn)
= (63)2/3 + (28)3/4 + (25)1/5
= 62 + 26 + 2 ..................................................................................................................... [(bn)m = bnm]
= 36 + 64 + 2
= 102.
Final Answer:-
∴ The given expression when simplified, gives the value 102.
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