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`