Question

Which expression is equivalent to (81x4y16)12 for all positive values of x and y?
40.5x4y16

Answer 1

`(81x^4y^(16))^{(1)/(2)} = 9 x^2 y^8`

Explanation:

Given

`(81x^4y^(16))^{(1)/(2)}`

Required

Determine an equivalent expression

Express 81 as
`9^2`

`(9^2x^4y^(16))^{(1)/(2)}`

Apply law of indices

`9^2^{(1)/(2)} * x^4^{(1)/(2)} * y^(16)^{(1)/(2)}`

`9^{(2*1)/(2)} * x^{(4*1)/(2)} * y^{(16*1)/(2)}`

`9^{(2)/(2)} * x^{(4)/(2)} * y^{(16)/(2)}`

`9^1 * x^2 * y^8`

`9 * x^2 * y^8`

`9 x^2 y^8`

Hence:

`(81x^4y^(16))^{(1)/(2)} = 9 x^2 y^8`