Exponent Rules

Exponent Rules

How can we apply rules of exponents?

Important Rules of Exponents

•  $x^{1\ }=\ x$  

• Example:  $3^{1\ }=\ 3$  

•  $x^{0\ }=\ 1$  

• Example:  $6^{0\ }=\ 1$  

Multiple Choice

Solve

 $4^1$  

• 4

• 1

• 0

Multiple Choice

Solve

 $4^0$  

• 4

• 1

• 0

Multiple Choice

Solve

 $9^1$  

• 9

• 0

• 1

Multiple Choice

Solve

 $100^1$  

• 100

• 0

• 1

Multiple Choice

Solve

 $25^0$  

• 25

• 1

• 0

Multiple Choice

Solve

 $4^0$  

• 4

• 1

• 0

Negative Exponents

Anytime an exponent is negative, we put it over 1 and make it positive.

If the base is a negative number it stays negative.

Only the exponents changes to positive.

Last step simplify

Evaluate

 $4^{-2}$  

• rewrite as  $\frac{1}{4^2}$  

• simplify  $\frac{1}{16}$  

Multiple Choice

Only re-write

 $6^{-3}$  

•  $\frac{1}{6^3}$  

•  $6^3$  

•  $\frac{1}{3}$  

Multiple Choice

Only re-write

 $-2^{-4}$  

•  $\frac{1}{-2^4}$  

•  $\frac{1}{2^4}$  

•  $\frac{1}{-2^{-4}}$  

Multiple Choice

Only re write

 $5^{-2}$  

•  $\frac{1}{5^{-2}}$  

•  $\frac{1}{2^5}$  

•  $\frac{1}{5^2}$  

Multiple Choice

Re write

 $-3^{-2}$  

•  $\frac{1}{3^2}$  

•  $\frac{1}{-3^2}$  

•  $\frac{1}{2^{-3}}$  

Evaluate

Remember to simplify your answer

Multiple Choice

 $5^{-2}$  

•  $\frac{1}{25}$  

•  $\frac{1}{5}$  

•  $\frac{1}{5^2}$  

Multiple Choice

 $3^{-3}$  

•  $\frac{1}{3}$  

•  $\frac{1}{27}$  

•  $\frac{1}{6}$  

Multiple Choice

 $-4^{-2}$  

•  $\frac{1}{16}$  

•  $\frac{1}{4}$  

•  $\frac{1}{-16}$  

Multiple Choice

 $-2^{-3}$  

•  $\frac{1}{-8}$  

•  $\frac{1}{8}$  

•  $\frac{1}{12}$  

Poll

Exit Slip: When you have a negative exponent, what do you do with it?

• Solve it

• put it under 1 and make the exponent positive then simplify.

• I slept all lesson. what?