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:

$\frac{y^{\frac{1}{2}}}{x}$

Answer:

$\frac{y^{\frac{1}{2}}}{x}$