Exponent laws part 1

Exponent laws part 1

Here we will be exploring what happens when we multiply and divide powers with the same base!

Multiple Choice

Write the following as a power:

 $2^5\times2^4$  

•  $2^1$  

•  $2^5$  

•  $2^9$  

•  $2^{20}$  

Multiple Choice

Write the following as a power:

 $5^5\times5^2$  

•  $5^3$  

•  $5^5$  

•  $5^7$  

•  $5^{10}$  

Multiple Choice

Write the following as a power:

 $\left(-3\right)^2\times\left(-3\right)^3$  

•  $\left(-3\right)^5$  

•  $3^5$  

•  $\left(-3\right)^6$  

•  $3^6$  

Multiple Choice

Write the following as a power:

 $10^5\times10$  

•  $10$  

•  $10^6$  

•  $10^5$  

•  $10^{10}$  

Multiple Choice

Write the following as a power:

 $\left(-5\right)^6\div\left(-5\right)^3$  

•  $\left(-5\right)$  

•  $\left(-5\right)^2$  

•  $\left(-5\right)^3$  

•  $\left(-5\right)^6$  

Multiple Choice

Write the following as a power:

 $\left(-3\right)^9\div\left(-3\right)^5$  

•  $\left(-3\right)^3$  

•  $\left(-3\right)^4$  

•  $\left(-3\right)^5$  

•  $\left(-3\right)^6$  

Multiple Choice

Write the following as a power:

 $8^4\div8^3$  

• 8

•  $8^2$  

•  $8^3$  

•  $8^4$  

Multiple Choice

Write the following as a power:

 $9^8\div9^2$  

•  $9^3$  

•  $9^4$  

•  $9^5$  

•  $9^6$  

Multiple Choice

Simplify to one power:

 $4\times4^3\div4^2$  

• 4

•  $4^2$  

•  $4^3$  

•  $4^4$  

Multiple Choice

Simplify into one power:

 $\left(-3\right)\div\left(-3\right)\times\left(-3\right)$  

• 1

•  $\left(-3\right)^2$  

• 3

• -3

PRACTICE

Now it's your turn to practice and review what we've learned!

Multiple Choice

True or false:

 $4^3\times4^5=4^{15}$  

• True

• False

Multiple Choice

Simplify

 $7^6\times7^2$  

•  $7$  

•  $7^6$  

•  $7^8$  

•  $7^{12}$  

Multiple Choice

Simplify

 $\left(-3\right)^4\times\left(-3\right)^5$  

•  $\left(-3\right)^4$  

•  $\left(-3\right)^5$  

•  $\left(-3\right)^9$  

•  $\left(-3\right)^{20}$  

Multiple Choice

 True or false: $10^6\div10^2=10^4$ 

• True

• False

Multiple Choice

Simplify $6^4\div6^4$  

•  $6^0$  

•  $6$  

•  $6^1$  

•  $6^4$  

Multiple Choice

Simplify $\left(-7\right)^8\div\left(-7\right)^4$  

•  $\left(-7\right)$  

•  $\left(-7\right)^2$  

•  $\left(-7\right)^3$  

•  $\left(-7\right)^4$  

Multiple Choice

Simplify: $10^3\times10^5\div10^2$  

•  $10^2$  

•  $10^4$  

•  $10^6$  

•  $10^{10}$  

Multiple Choice

Simplify: $\left(-1\right)^8\div\left(-1\right)^3\times\left(-1\right)^1$  

•  $\left(-1\right)$  

•  $\left(-1\right)^3$  

•  $\left(-1\right)^5$  

•  $\left(-1\right)^6$  

In summary:

When we multiply powers with the same base, we can add the exponents:

 $a^n\times a^m=a^{n+m}$  

When we divide powers with the same base, we can subtract the exponents:
 $a^n\div a^m=a^{n-m}$  
We can also combine the 2 to make one simplified power!