Question

if x=2^2n
find,
8*x^3/2n - 8*x^-3/2n

Answer 1

(x^a)^b = x^(ab)

Similarly in this case, x = 2^(2n)

And we are supposed to calculate the value of the given expression,

8^(3/2n) - 8 * x^(-3/2n)

First we'll calculate the value of,

x^(-3/2n) = (2^2n)^(-3/2n) = 2^(2n * (-3/2n))

= 2^(-3) = 1/8.

So our expression becomes,

8^(3/2n) - 8 * 1/8 = 8^(3/2n) - 1

= 512^(1/2n) - 1.

Since we don't know the value of n, this is our final answer.

Unless, of course, I have made some mistake reading the question, for which I'll apologize.

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