In week 2 of Precalc 11 we focused on fractional exponents and being able to solve questions where the exponents are positive and negative.  When you have a number with an exponent that is 1/2, it will always be the square root of the number. For example if you have 100^1/2 it would be 10 because 10×10=100. There is a similar rule for if you have an exponent that is 1/3 , it will always be the cubed root of the number. For example 64^1/3 it would be 4 because  4x4x4=64. Those rules only apply if you have an exponent of 1/2 or 1/3, if you had a different fraction you have to put a little more work into it. If you have a question that is 25^3/2 you will have to look at the different parts of the question. The bottom of the fraction indicates that it will be the index or root and the top of the fraction indicates the exponent. So you would first have to solve the square root of 25 which is 5 and then you would have to do 5 to the power of 3 which is 5x5x5=125. All those questions were dealing with positive fractional exponents, but not all of them are positive. The first rule of having a negative exponent is to reciprocate the fraction to make the exponent a positive. If you have a question that is 4^-3  then you would change it to 1/4^3 which would be 1/64. If you have a negative fractional exponent you would do the same steps as you would with a positive exponent except you would start by reciprocating the fraction. If you had 8^-2/3 you would change it to 1/8^2/3 and then find the cubed root of 8 which is 2 and then you would do 2 to the power of 2 which would give you 1/4.