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Question
Assuming that x, y, z are positive real numbers, simplify the following:
`sqrt(x^3y^-2)`
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Solution
We have to simplify the following, assuming that x, y, z are positive real numbers
Given `sqrt(x^3y^-2)`
As x and y are positive real numbers then we can write
`sqrt(x^3y^-2)=(x^3y^-2)^(1/2)`
`=(x^(3xx1/2)xxy^(-2xx1/2))`
`=(x^(3/2)y^-1)`
By using law of rational exponents `a^-n=1/a^n` we have
`sqrt(x^3y^-2)=x^(3/2)xx1/y`
`=x^(3/2)/y`
Hence the simplified value of `sqrt(x^3y^-2)` is `x^(3/2)/y`
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