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

1 Answer
Aug 26, 2016

Answer:

#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)#