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Question
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
Solution
We have to simplify the following, assuming that x, y, z are positive real numbers
Given `(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
`=(x^(1/2))^(-2/3)(y^4)^(1/2)div(x xxy^(-1/2))^(1/2)`
`=(x^(1/2xx-2/3)xxy^(4xx1/2))/(x^(1/2)xxy^(-1/2xx1/2))`
`=(x^(-1/3)xxy^2)/(x^(1/2)xxy^(-1/4))`
By using the law of rational exponents, `a^mdiva^n=a^(m-n)` we have
`=x^(-1/3-1/2)xxy^(2+1/4)`
`=x^(-5/6)xxy^(9/4)`
`=1/x^(5/6)xxy^(9/4)`
`=y^(9/4)/x^(5/6)`
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