Indicies help!!!!?

Question

x to the power of -1/2

what does this mean

Answer 1

x^(-1/2) = 1 / x^(1/2)
Example
16^(-1/2) = 1 / 16^(1/2) = 1 / 4

Answer 2

Let me explain properties you will be using here.

Let's start with the negative exponent.
a^(-n) = 1/(a^n) example: 2^-3 = 1/2^3 = 1/8

therefore now we get:
1/(x^1/2)

let's move to the rational exponents:
x^(m/n) = n-th root (x^m)
therefore x^1/2 = square root of x to the power of 1. x^1/2 = sqrt(x)

1/sqrt(x) is what we are having now. Now you should rationalize the denominator by multiplying the denominator and the numerator by sqrt(x)

your final answer will be:
sqrt(x)/x

Answer 3

1 over square root of x.

Answer 4

x^-1/2 = 1/(x^1/2) or 1/sqrt(x)