13+-+Sec.+8.1A

Multiplication Properties of Exponents 8.1A

By: Brandon Julian and John Nguyen

Goal 1: What you should learn... How to use the multiplication properties of exponents to evaluate powers and simplify expressions.
 * Multiplying the Exponents**

Goal 2: How to use powers and the exponential change equation as models in real-life settings.

Why should I learn it: You can use exponents in models of real-life situations that involve exponential change, and for repeated factors, such as in formulas for area and volume. This also helps you calculate the generated power given from a windmill. Learning how to solve properties of exponents are very important because this can help you in life.[|Practice Problems]

To multiply two powers that have the same number, you add the exponents. To see if this is true, watch what happens when you multiple b 2 and b 3 can also be written as b x b x b x b x b because when you add the two exponents together they equal 5, so you write "b" times itself 5 times. Example 1: b 2 x b 3 b x b x b x b x b b 2+3 = b5
 * To multiply powers with the same letter, add the exponents to get the answer.**

c m x c n = c m+n y 6 x y 7 x y 8 = y 6+7+8 = y 22 = = (-4)(-4) 9 = (-4)​ 10
 * Power of Power Properties**

(c a ) b = c ab

(a^m)^n= a^m^n (3^4)^2= 3^8 (2^5)^3= 2^15 [(-6)^2]^5= (-6)^10
 * To find the power of a power, multiply exponents.**

Extra problems:

(2a^2b)(3ab)(5ab^2)= 30a^4b^4

(a^2b)^3(-2ab^2)= (a^6b^3)(-2ab^2)= -2a^7b^5

n^3 x n^2 = n^5

4^2 x 4^5 =4^7

Simplify. 1. (a 5 ) 7
 * Practice Problems**

2. (3x 2​ )​ 5​