Question

Which expresion is equivalent to (x1/2y-1/4)-2

Answer 1

For this case we must find an expression equivalent to:

`(x ^ {\frac {1} {2}} * y ^ {-\frac {1} {4}})^(-2)`

By definition of power properties we have to:

`(a ^ n) ^ m = a ^ {n * m}`

So:

`x ^ {\frac {1 * -2} {2}} * y ^ {-\frac {1 * -2} {4}} =\\x ^ {\frac {-2} {2}} * y ^ {\frac {2} {4}} =\\x ^ {-1} *y ^ {\frac {1} {2}}`

We have by definition of properties of powers that:
`a ^ {-1} = \frac {1} {a ^ 1} = \frac {1} {a}`

Then, rewriting the expression:

`\frac{y^{(1)/(2)}}{x}`

Answer:

`\frac{y^{(1)/(2)}}{x}`