# What is x: x^5/2 = 1/32

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll consider that the power of x is 5/2.

We'll re-write as a power of two the right side:

1/32 = 1/`2^5` = `2^-5`

Now, we'll re-write the equation:

` x^(5/2) = 2^-5 `

We'll raise both sides to the power (2/5), to eliminate the rational power of x from the left side:

`x^[(5/2)*(2/5)]= (2^-5)^(2/5)`

x = `2^-2 `

We'll use the negative power property:

x = 1/`2^2`

x = 1/4

The solution of the given equation is x = 1/4.