Question

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

Answer 1

x^1/8y^8

Explanation:

Answer 2

expression is equivalent to
`(x^{(1)/(4)} y^(16))^{(1)/(2)}`

We apply exponential property

Multiply the outside exponent 1/2 with exponents inside the parenthesis

`(x^{(1)/(4)} y^(16))^{(1)/(2)}`

`(x^{(1)/(4)*(1)/(2)} y^{16*(1)/(2)})`

1/4 times 1/2 is 1/8

16 times 1/2 is 8

so expression becomes

`(x^{(1)/(8)} y^(8))`

So the answer is

`(x^{(1)/(8)} y^(8))`