Question

Which expression is equivalent to (x^1/4 y^16) ^1/2

Answer 1

For this case we must indicate an expression equivalent to:

$(x ^ {\frac {1} {4}} * y ^ {16}) ^ {\frac {1} {2}}$

By definition of power properties we have:

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

We can rewrite the expression as:

$((x ^ {\frac {1} {4}}) ^ {\frac {1} {2}}) * ((y ^ {16}) ^ {\frac {1} {2}}) =\\x ^ {\frac {1} {8}} * y ^ 8$

Answer:

$x ^ {\frac {1} {8}} * y ^ 8$