Zeroth Power

Zeroth Power

What we already know about exponents

•  $x^m\cdot x^n=x^{m+n}$  

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

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

•  $\frac{x^m}{x^n}=x^{m-n}$  

Open Ended

What should

 $3^0$  equal?

 $x^{0\ }=\ 1$  

Multiple Choice

 $x^0\cdot x^n$  

•  $x^n$  

• 1

Multiple Choice

 $x^0\cdot x^0$  

• 0

• 1

Multiple Choice

 $\left(x^o\right)^n$  

• 1

•  $x^n$  

Multiple Choice

 $\left(x^0\right)^0$  

• 1

• x

Multiple Choice

 $\left(x\cdot y\right)^0$  

•  $x\cdot y$  

• 1

Expanded Form

Final Questions

Open Ended

Simplify as much as possible:

 $\frac{4^{10}}{4^{10}}\cdot7^0$  

Explain why

 $\left(a^0+b^0\right)a^0$  and  $\left(a^0+b^0\right)b^0$  
are equal

Hint: Use the distributive law and the definition of the zeroth power