Question

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

Answer 1

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

Explanation:

Consider the given expression

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

According to the distributive property of exponent,

`(ab)^m=a^mb^m`

Using distributive property of exponent we get

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

Using the property of exponent we get

`x^{(1)/(4)* (1)/(2)}y^{16* (1)/(2)}`
`[\because (a^m)^n=a^(mn)]`

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

Therefore, the expression
`x^{(1)/(8)}y^(8)` is equivalent to the given expression.

Answer 2

Equivalent expression is
`x^{(1)/(8)}y^(8)`

Explanation:

Given Expression is

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

We have to find Equivalent expression to given expression.

using law of exponent ,
`(ab)^x=a^xb^x`

we get,

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

now using another law of exponent,
`(x^a)^b=x^(ab)`

we get,

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

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

Therefore, Equivalent expression is
`x^{(1)/(8)}y^(8)`