Exponents/Powers

In this section, you will find the Laws of Exponents, examples, and also an interactive quiz. Enjoy!

If you need to practice more, here is a randomly generated worksheet.

Definition:

$a^n$= $a*a*a*a$..., that is, the number written in the upper right-hand corner is called the exponent or power, and it tells how many times the other number (called the base) is multiplied times itself. If an exponent cannot be seen, it equal 1.

Ex: $5^6 = 5*5*5*5*5*5=15,625$.

Rule: $a^n * a^m = a^{m+n}$ ; that is, when multiplying the same base, the new exponent can be found by adding the exponents of the bases that are multiplied.

• $(5^3)(5^4)=5^7$
• $(x^2)(x)=x^3$

Rule: $a^n/a^m = a^{n-m}$; that is, when dividing the same base, the new exponent can be found by subtracting the exponents of the bases that are divided. The new base and exponent go either in the numerator or in the denominator, wherever goes the highest exponent was located in the original problem. Remember the signs' laws.

Ex:
• $(7^5)/(7^2)=7^3$
• $(3^4)/(3^6)=3^(-2)=1/(3^2)$

Rule: $a^{-n}=1/a^n$; that is, a negative exponent can be changed to a positive exponent by moving the base to the other section of the fraction; numerator goes to denominator or denominator goes to numerator.

Ex:
• $7^{-3}=1/(7^3)$
• $(3^4)/(3^6)=3^(-2)=1/(3^2)$