Question

What is the value of the expression below? (9^2) ^1/4

Answer 1

3

EXPLANATION

The given expression is

`{(9}^(2) )^{ (1)/(4) }`

Recall and use the property:

`({a}^(m))^(n) = {a}^(mn)`

`= {(9})^{ 2 * (1)/(4) }`

`= {9}^{ (1)/(2) }`

`= √(9)`

`= 3`

Answer 2

3

Explanation:

1. Note that
`9=3^2.`

2. Use property
`(a^m)^n=a^(m\cdot n),` then

`9^2=(3^2)^2=3^(2\cdot 2)=3^4.`

3. Use the same property, thus

`(9^2)^{(1)/(4)}=(3^4)^{(1)/(4)}=3^{4\cdot (1)/(4)}=3^1=3.`