Question

What is the value of the exponential expression 36 1/2

Answer 1

The value of the given exponential expression
`36^{(1)/(2)}\:` is 6.

Explanation:

Given: the exponential expression
`36^{(1)/(2)}\:`

We have to find the value of the given exponential expression
`36^{(1)/(2)}\:`

Consider the given exponential expression
`36^{(1)/(2)}\:`

We know
`√(x)=x^{(1)/(2)}`

Thus,
`36^{(1)/(2)}=√(36)`

Factor the number 36 as
`36=6^2`

`\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a`

we have,

`√(6^2)=6`

Thus, the value of the given exponential expression
`36^{(1)/(2)}\:` is 6.

Answer 2

For this case we have an exponential expression of the form:

`36^{ (1)/(2)}`
We can rewrite the exponential expression using power properties.
We have then:

`√(36)`
From here, we take the square root of 36.
We have then:

`√(36) = 6`
Answer:
The exponential function is given by:

`36^{ (1)/(2)}=6`