Laws of Exponents

Laws of Exponents

Parts of an Exponents

Base: the number you are multiplying by itself

Exponent: the number of times a number is ultiplied by itself

Law One

 $x^{n\ }=\ x\cdot x\cdot x\cdot x...\cdot x$  

Multiple Choice

 $5^{4\ }=$  

•  $5\cdot5\cdot5\cdot5$  

•  $5\cdot4$  

Law 2

 $x^{0\ \ }=\ 1\$  
Any base (except 0) raise to the zero power is 1. 

Fill in the Blank

Any base raised to the zero power is 1, except which value?

Law 3

 $x^1=x$  
Any base raised to the power of one is itself. 

Multiple Select

Select all that are true.

• $k^{1\ }=k$

• $100^{1\ }=\ 100$

• $6^1=\ 6$

• $3^1=1$

Law 4

 $x^m\cdot x^n=\ x^{\ m+n}$  


To multiply two same bases, write the base and ADD the exponents. 

Multiple Choice

 $4^2\cdot4^6$  

•  $4^{2\cdot6\ }=\ 4^{12}$  

•  $4^{2+6\ }=\ 4^8$  

Law Five

 $\frac{x^m}{x^n}=\ x^{\ m-n}$  

To divide when two bases are the same, write the base and SUBTRACT the exponents. 

Open Ended

When dividing two bases that are the same, what operation is performed on the exponents?

Law 6

 $\left(x^m\right)^n=\ x^{m\cdot n}$  

To raise a power to another power, write the base and MULTIPLY the exponents. 

Law 7 

 $\left(xy\right)^m=x^my^m$  

To raise different bases to the same power, DISTRIBUTE the exponent to both bases. 

Multiple Choice

 $\left(3d\right)^3$  

•  $3d^3$  

•  $9d^3$  

p2 Law 7

 $\left(\frac{x}{y}\right)^m=\frac{x^m}{y^m}$  

To raise different bases to the same power, DISTRIBUTE the exponent to both bases. 

Multiple Choice

 $\left(\frac{w}{2}\right)^2$  

•  $\frac{w^2}{2}$  

•  $\frac{w^2}{2^2}$  

Law 8

 $x^{-m}=\ \frac{1}{x^m}$  

If a factor in the numerator or denominator is moved across the fraction bar, the exponent sign changes. 

Multiple Choice

How do you elevate (get rid of ) a negative exponent?

• Move it across the fraction bar.

• Ask it nicely to leave.

p2 Law 8

 $\frac{1}{x^{-m}}=x^m$  

Multiple Choice

 $\frac{1}{6^{-7}}$  

•  $6^7$  

•  $6-7=-1$  

p3 Law 8

 $\left(\frac{x}{y}\right)^{-n}=\left(\frac{y}{x}\right)^n$  

Multiple Choice

Which of the following is not true solution for $\left(\frac{8}{j}\right)^{-2}$ ? 

•  $\frac{8^2}{j^2}$  

•  $\left(\frac{j}{8}\right)^2$  

•  $\frac{j^2}{64}$  

*Law 9

 $x^{\frac{1}{n}}=^n\sqrt{x}$  

Multiple Choice

 $c^{\frac{1}{4}}$  

•  $c^4$  

•  $^4\sqrt{c}$  

*p2 Law 9

 $x^{\frac{m}{n}}=^n\sqrt{x^m}$