Properties of Exponents

Properties of Exponents

Let's learn the properties of exponents. You'll want to take notes as you go so that you can answer all of the questions.

Product of Powers

 $a^n\cdot a^m=a^{n+m}$  

Product of Powers: Example

 $x^3\cdot x^2=x^{2+3}=x^5$  

Multiple Choice

Your turn: product of powers. What is $y^6\cdot y^2$ ?

•  $y^{6+2}$  

•  $y^{6-2}$  

•  $y^{6\div2}$  

•  $y^{6\times2}$  

Multiple Choice

 $z^3\cdot z^7=?$  

•  $z^{21}$  

•  $z^{\frac{3}{7}}$  

•  $z^{-4}$  

•  $z^{10}$  

•  $z^4$  

Power of a Product

 $\left(ab\right)^m=a^mb^m$  

Power of a Product: Example

 $\left(3xy\right)^2=3^2x^2y^2=9x^2y^2$  

Multiple Choice

Now it's your turn. $\left(2ab\right)^3=?$  

•  $2xy$  

•  $2x^3y^3$  

•  $8xy$  

•  $8x^3y^3$  

Power of a Power

 $\left(a^n\right)^m=a^{n\cdot m}$  

Power of a Power: Example

 $\left(w^5\right)^3=w^{5\cdot3}=w^{15}$  

Multiple Choice

Now it is your turn. $\left(t^6\right)^9=?$  

•  $t^{15}$  

•  $t^3$  

•  $t^{-3}$  

•  $t^{\frac{1}{3}}$  

•  $t^{54}$  

Power of a Zero

 $a^0=1$  . It doesn't matter what a is. 

Power of a Zero: Examples.

 $1^0=1$        $3^0=1$  

 $2^0=1$        $4^0=1$  
        $5000^0=1$  
EVERYTHING TO A POWER OF ZERO EQUALS ONE!!!

Quotient of Powers

 $\frac{a^n}{a^m}=a^{n-m}$  

Quotient of Powers: Example.

 $\frac{\left(6c\right)^8}{\left(6c\right)^4}=\left(6c\right)^{8-4}=\left(6c\right)^4=24c^4$  

Multiple Choice

Your turn. What is $\frac{\left(2x\right)^5}{\left(2x\right)^3}=?$  

•  $4x^2$  

•  $8x^2$  

•  $1$  

•  $16x^8$  

Power of a Quotient

 $\left(\frac{a}{b}\right)^m=\frac{a^m}{b^m}$  

Power of a Quotient: Example

 $\left(\frac{5x}{2y}\right)^3=\frac{\left(5x\right)^3}{\left(2y\right)^3}=\frac{125x^3}{8y^3}$  

Multiple Select

Now it is your turn. $\left(\frac{2s}{r}\right)^4=?$  Select all that are right.

•  $\frac{\left(2s\right)^4}{r^4}$  

•  $\frac{16s^4}{r^4}$  

•  $\frac{8s^4}{r^2}$  

• Cannot be simplified

Negative Exponents.

 $a^{-n}=\frac{1}{a^n}$  

Negative Exponents Examples.

 $w^{-6}=\frac{1}{w^6}$    

  $c^{-1}=\frac{1}{c^1}=\frac{1}{c}$  

Multiple Choice

Your turn. What is $y^{-12}?$  

•  $y^{12}$  

•  $\frac{1}{y^6}$  

• Cannot be simplified. 

•  $\frac{1}{y^{12}}$