Question

Please help me to solve this problem of ordered pairs. The value of x and y should be find. ​

Answer 1

x = y = - 2

Explanation:

Using the rule of radicals/ exponents

`a^{(m)/(n) }` =
`\sqrt[n]{a^(m) }` ,
`a^(-m)` =
`(1)/(a^(m) )` ,
`(a^m)^(n)` =
`a^(mn)`

Given

`\sqrt[x]{4}` =
`(1)/(2)` , then

`\sqrt[x]{2^(2) }` =
`(1)/(2)`

`2^{(2)/(x) }` =
`2^(-1)`

Since the bases on both sides are equal, both 2 , then equate exponents

`(2)/(x)` = - 1 ( multiply both sides by x )

2 = - x , that is

x = - 2

Similarly

`\sqrt[y]{9}` =
`(1)/(3)` , then

`\sqrt[y]{3^(2) }` =
`(1)/(3)`

`3^{(2)/(y) }` =
`3^(-1)`

Equating the exponents gives

`(2)/(y)` = - 1 ⇒ - y = 2 ⇒ y = - 2

Answer 2

x=y=-2

Explanation:

Comparing these ordered pairs, we will get

4^(1/x)=1/2 and 9^(1/y)=1/3

x=-2 and y=-2