Question

How do you write `5^-6` with positive exponents?

Answer 1

`5^-6 =1/5^6`

Explanation:

One of the laws of indices states:

`x^color(red)((-m)) = 1/x^color(red)((+m))`

We can see that when the base of `x` was moved from the numerator to the denominator, the sign of the index changed.

The same will happen if a base is moved from the denominator to the numerator.

`1/x^color(blue)((-n)) = x^color(blue)((+n))`

`5^-6 =1/5^6`

Note:

• This is better written in this form, rather than `1/15625`

• This has nothing to do with the negative numbers like `-5 or -8` on the number line!

• Only the base with the negative index is moved. All the other numbers and bases stay the same.

`2x^3color(red)(y^-4) = (2x^3)/color(red)(y^4)`