Laws of Exponents

Laws of Exponents

Ms. Randolph's Class Notes

Exponents Review - No need to write down

• Tell us how many times to multiply a number by itself

• For example,

• 4² means we do 4 x 4, which is 16

• 4³= 4 x 4 x 4 = 64

Zero Exponent Rule

• Anything raised to the 0 power is 1

• Ex. 1: 4⁰=1

• Ex. 2: 1,000⁰=1

• Ex. 3: x⁰=1

Multiple Choice

What is 100⁰?

• 0

• 1

• 100

Product Rule

• To multiply exponents with the same base, add the exponents

• Ex. 1: 5³ x 5⁴ =

• Ex. 2: 1,000² x 1,000³ =

• Ex. 3: y⁵ x y³ =

Multiple Choice

What is m⁴ x m⁶ ?

• m⁴⁶

• m²⁴

• m¹⁰

• Unable to solve

Quotient Rule

• To divide exponents with the same base, subtract the exponent

• Ex. 1:  $\frac{4^5}{4^3}=$  

• Ex. 2:  $10^{11}\div10^6=$  

• Ex. 3:  $\frac{a^9}{a^2}=$  

Multiple Choice

What is 

 $\frac{5^{15}}{5^5}$  ?

•  $5^{20}$  

•  $5^{10}$  

•  $5^{15}$  

•  $5^{155}$  

Power Rule

• To raise a power to a power, multiply the powers

• Ex. 1: (4³)²=

• Ex. 2: (3⁵)⁶=

• Ex. 3: (p⁴)³ =

Multiple Choice

What is (y⁴)⁵

• y²⁰

• y⁵

• y⁹

• y¹

Negative Exponent Rule

• A number raised to a negative exponent is the same as the reciprocal of the number raised to a positive exponent

• Ex. 1:  $2^{-3}=$  

• Ex. 2:  $4^{-2}=\$  

• Ex. 3:  $\left(\frac{2}{3}\right)^{-5}=$  

• Ex. 4:  $x^{-3}=$  

Multiple Choice

Which is equivalent to

 $\left(\frac{2}{5}\right)^{-3}$  ?

•  $\left(\frac{2}{5}\right)^3$  

•  $\left(\frac{5}{2}\right)^{-3}$  

•  $2^3$  

•  $\left(\frac{5}{2}\right)^3$  

Let's Practice!

With guidance

Multiple Choice

Using the product rule, which is equivalent to

 $4^5\times4^3$  ?

•  $4^8$  

•  $4^{15}$  

•  $4^6$  

•  $4^2$  

Multiple Choice

Using the product rule, which is equivalent to

 $y^4\times y^3$  ?

•  $y^{12}$   

•  $y^1$  
  

•  $y^7$  

  
  

Multiple Choice

Using the quotient rule, which is equivalent to

 $6^3\div6^2$  ?

•  $6^5$  

•  $6^6$  

•  $6^1$  

•  $6^2$  

Multiple Choice

Using the quotient rule, which is equivalent to

 $\frac{y^{10}}{y^3}$  ?

•  $y^7$  

•  $y^2$  

•  $y^{13}$  

•  $y^6$  

Multiple Choice

Using the power rule, which is equivalent to

 $\left(3^4\right)^5$  ?

•  $3^9$  

•  $3^{20}$  

•  $3^1$  

•  $3^{18}$  

Multiple Choice

Using the power rule, which is equivalent to

 $\left(x^2\right)^{10}$  ?

•  $x^8$  

•  $x^{22}$  

•  $x^{12}$  

•  $x^{20}$  

Multiple Choice

Using the negative exponent rule, which is equivalent to

 $2^{-8}$  ?

•  $\frac{1}{2^{-8}}$  

•  $\frac{1}{2^8}$  

•  $2^8$  

• Unable to solve

Multiple Choice

Using the negative exponent rule, which is equivalent to

 $\left(\frac{6}{7}\right)^{-4}$  ?

•  $\left(\frac{6}{7}\right)\ ^4$  

•  $\left(\frac{7}{6}\right)^4$  

•  $6^4$  

•  $\left(\frac{7}{6}\right)^{-4}$  

Multiple Choice

What is the value of 7⁰

• 7

• 1

• 5

• 70