Question

Compute the sum of [27/64]^-2/3​

Answer 1

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Answer 2

Answer:As the power is negative so we will do the reciprocal of the base that is 27/64 as 64/27.Next step is to write 64 and 27 in exponential form .As 64 can be written as (8)^2 and 27 as (3)^3.Now again we can write 8 as (2)^3,so 64 becomes (2)^6 and 27 is already (3)^3..

Now we have to solve [(2)^6/(3)^3]^2/3

We can write it as,{[(2)^6]^2/3}/{[(3)^3]^2/3},

Now on solving 6×2/3 =4 so it becomes (2)^4

On solving 3×2/3 =2, so it becomes (3)^2

So we get (2)^4/(3)^2,

(2)^4 is 16 and (3)^2 is 9 so the answer becomes 16/9 ,but 16 is (4)^2 and 9 is (3)^2

By cutting both 2 we get 4/3 as the answer.

Step-by-step explanation: