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Question
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
Solution
We have to simplify the following, assuming that x, y, z are positive real numbers
Given `(sqrt(x^-3))^5`
As x is positive real number then we have
`(sqrt(x^-3))^5=(sqrt(1/x^3))^5`
`=(sqrt1/sqrt(x^3))^5`
`=(1/x^(3xx1/2))^5`
`=(1/x^(3/2))`
`(sqrt(x^-3))^5=(1^5/x^(3/2xx5))`
`=1/x^(15/2)`
Hence the simplified value of `(sqrt(x^-3))^5` is `1/x^(15/2)`
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