Exponents often times scare the bejeezus out of students. The word exponent alone conjures up numbers so big that they seemingly dwarf the number of atoms in the known universe. But do not fear: there are no atoms on the test, and the exponents on the SAT deal with far smaller numbers. Below are a few important things you need to know about exponents.
- n^x = n times itself x times
This probably sounds scarier than it really is. For example, 2^3 = 2 x 2 x 2 = 8. There is also some quick terminology you should know. n is called the base and x is called the exponent. In our example, 2 is the base and 3 is the exponent.
- When multiplying exponents always add: (n^x)(n^x) = n^ (x + x)
When multiplying exponents it is very important to make sure the bases are the same. Notice how each base is ‘n’. So (3^3)(3^2) = 3^5 (remember to add exponents). But if we have (3^5)(2^3) we cannot add exponents but must leave the number as is.
- When ‘exponent-ing’ exponents always multiply: (x^n)^m equals x^(nm)
This is a classic the SAT uses almost every time. Students think that (3^2)^3 = 3^8 (refers back to the 2^3 from the last example). But instead of taking 2^3 we want to multiply 2 x 3 = 6.
So when you have a parenthesis around the base and an exponent, the exponent on the inside of the parenthesis is multiplied times the exponent on the outside of
By remembering these three points on exponents you will be able to solve almost every question on the test. Good luck!