Product and Power Properties of Exponents

Properties of Exponents

Let's review the properties of exponents. You'll want to take notes as you go so that you can answer all of the questions.

​Exponents

Remember:

Invisible ones!

5 = 5¹
x = x¹

Product of Powers

Product of Powers: Example

Multiple Choice

Your turn: product of powers. What is $$y^6\cdot y^2$$ ?

• $$y^{6+2}$$  

• $$y^{6-2}$$  

• $$y^{6\div2}$$  

• $$y^{6\times2}$$  

Multiple Choice

$$z^3\cdot z^7=?$$  

• $$z^{21}$$  

• $$z^{\frac{3}{7}}$$  

• $$z^{-4}$$  

• $$z^{10}$$  

• $$z^4$$  

Power of a Product

Power of a Product: Example

Multiple Choice

Now it's your turn. $$\left(2ab\right)^3=?$$  

• $$2xy$$  

• $$2x^3y^3$$  

• $$8xy$$  

• $$8x^3y^3$$  

Power of a Power

Power of a Power: Example

Multiple Choice

Now it is your turn. $$\left(t^6\right)^9=?$$  

• $$t^{15}$$  

• $$t^3$$  

• $$t^{-3}$$  

• $$t^{\frac{1}{3}}$$  

• $$t^{54}$$  

Power of a Zero

Power of a Zero: Examples.

Quotient of Powers

Quotient of Powers: Example.

Multiple Choice

Your turn. What is $$\frac{\left(2x\right)^5}{\left(2x\right)^3}=?$$  

• $$4x^2$$  

• $$8x^2$$  

• $$1$$  

• $$16x^8$$  

Power of a Quotient

Power of a Quotient: Example

Multiple Select

Now it is your turn. $$\left(\frac{2s}{r}\right)^4=?$$  Select all that are right.

• $$\frac{\left(2s\right)^4}{r^4}$$  

• $$\frac{16s^4}{r^4}$$  

• $$\frac{8s^4}{r^2}$$  

• Cannot be simplified

Negative Exponents.

​FLIP!

Negative Exponents Examples.

​FLIP!

​FLIP!

Multiple Choice

Your turn. What is $$y^{-12}?$$  

• $$y^{12}$$  

• $$\frac{1}{y^6}$$  

• Cannot be simplified. 

• $$\frac{1}{y^{12}}$$  

​In Summary: