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Could you show me how this is done. I've been having some trouble understanding the subtracting and adding of these types.

calculate: 2^(5/2)-2^(3/2)

Hi Angelo,

Basically, X^a - X^b = X^b . [X^(a-b) - 1]

2^(5/2) - 2^(3/2) = 2^(3/2) . [2^(5/2 - 3/2) - 1]

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

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

= 2^(3/2)

Notice that 2^(5/2) is twice 2^(3/2) i.e

2^(5/2) = 2 . [2^(3/2)]

On another hand, 2^3 is the square of 2^(3/2) i.e

2^3 = [2^(3/2)]^2

since

(X^a)^b = X^(ab)

Regards

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