Multiplying Exponents

Multiplying Exponents

Take a look at this pattern...

 $2^2=\left(2\cdot2\right)\ =\ 4$  

 $3^4=\left(3\cdot3\cdot3\cdot3\ \right)=\ 81$  

 $5^3=\left(5\cdot5\cdot5\right)\ =\ 125$  

Multiple Choice

Select the correct answer:

 $6^3\ =\ \left(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \right)?$  

•  $3\cdot3\cdot3\cdot3\cdot3\cdot3$  

•  $6\cdot6$  

•  $6\cdot6\cdot6$  

Multiple Choice

 Complete... (Use your calculator)

 $6^3\ =\ \left(6\cdot6\cdot6\right)\ =\ ?$ 

• 216

• 18

• 36

Multiple Choice

Complete:

 $2^5\ =\ \left(\ \ \ \ \ \ ?\ \ \ \ \ \ \right)\ =\ ?$  

•  $\left(2\cdot2\right)\ =\ 4$  

•  $\left(2\cdot2\cdot2\cdot2\cdot2\right)=\ 32$  

•  $\left(5\cdot5\right)=25$  

We can also multiply exponents of the SAME BASE together. Look at these examples...


 $\ \ \ \ \ \ 5^2\ \ \ \ \ \ \ \ \ \ \cdot\ \ \ \ \ \ \ \ \ 5^3$ 
 $=5\cdot5\ \ \ \ \ \ \ \cdot\ \ \ \ \ \ \ \ 5\cdot5\cdot5$  

 $=\ 5\cdot5\cdot5\cdot5\cdot5$  

Multiple Choice

... and how can we rewrite

 $5\cdot5\cdot5\cdot5\cdot5$  ?

•  $5^3$  

•  $5^2$  

•  $5^5$  

Multiple Choice

How can we rewrite the following... ?


 $8^{4\ }\cdot\ \ 8^2$  

•  $8\cdot8\cdot8\cdot8\ \ \ \ \ \ \ \ \cdot\ \ \ \ 8\cdot8$  

•  $8\cdot8\ \ \ \ \ \ \ \cdot\ \ \ \ 8$  

•  $8\cdot8\cdot8\cdot8\cdot8$  

Multiple Choice

... and how can we rewrite

 $8\cdot8\cdot8\cdot8\ \ \ \ \ \ \ \ \cdot\ \ \ \ \ \ \ 8\cdot8$      ?

•  $8^2$  

•  $8^6$  

•  $8^4$  

Variable exponents work the same way... Take a look at the pattern... What do you notice?

 $x^2=x\cdot x$  
 $y^5\ =\ y\cdot y\cdot y\cdot y\cdot y$  

 $n^7=\ n\cdot n\cdot n\cdot n\cdot n\cdot n\cdot n$  

Multiple Choice

Rewrite  $e^5$  

•  $e\cdot e$  

•  $e\cdot e\cdot e$  

•  $e\cdot e\cdot e\cdot e\cdot e$  

Multiple Choice

rewrite $y\cdot y\cdot y\cdot y\cdot y\cdot y$  

•  $y^3$  

•  $y^9$  

•  $y^6$  

Check it out... We can multiply variable exponents the same way as before... $x^3\ \ \ \ \ \ \cdot\ \ \ \ \ \ \ x^2$  

 $=x\cdot x\cdot x\ \ \ \ \ \ \ \cdot\ \ \ \ \ \ x\cdot x$  
= $x\cdot x\cdot x\cdot x\cdot x$  
= $x^5$  

Multiple Choice

x⁴ (x¹²)

• x³
• x⁴⁸
• x¹⁶
• x⁸

Multiple Choice

Simplify
m⁵⋅m²

• m⁷
• m³
• m¹⁰
• m²

Multiple Choice

r²⋅ r

• r³

• r²

• 2r³

• 11r²

Multiple Choice

r²⋅ r

• r³

• r²

• 2r³

• 11r²