3/17 Alg1: Properties of Exponents

3/17 Wednesday

Algebra 1

Morning Message

Good morning! Happy Saint Patrick's Day!

How was everyone's half day? Today we are working on our ability to solve equations with rational exponents. This type of problem solving is really an extension of our understanding of exponent rules and solving equations for x. Let's use what we know! :)

Announcements:

I have office hours until 3:40. Let me know ahead of time if you plan on visiting me, please.

We have two virtual half days Thursday and Friday. I won't see you tomorrow!

Agenda

• Learning Target

• Review of writing radicals using rational exponents

• Do Now review

• Solving equations using rational exponents

• Debrief

• Exit Ticket

Poll

Please rate your current state of understanding of the learning target.

Learning Target: I can solve equations with rational exponents.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there.

• 1 - I don't understand, I need some more help.

What does  $3^{\frac{1}{2}}$  equal?

What do you think? You can answer on the next slide.

Multiple Choice

What does  $3^{\frac{1}{2}}$  equal?

• 1.5

• 6

• 3

•  $\sqrt{3}$  

Recall your Do Now

What is the answer?

Multiple Choice

What does $2^{\frac{1}{3}}$  equal?

• 2

•  $\sqrt{2}$  

• 8

Let's work more with our properties of exponents and see how they work with rational exponents.

Multiple Choice

Consider the equation $\left(3^{\frac{x}{2}}\right)\left(3^{\frac{x}{3}}\right)=3^9$  .

Which property of exponents does this look like we will use to solve for x?

• Power of a power

• Power of a product

• Product of powers

• Quotient of powers

Multiple Choice

Consider the equation $\left(3^{\frac{x}{2}}\right)\left(3^{\frac{x}{3}}\right)=3^9$  .

What does the product of powers property tell us to do first if we want to solve for x?

• Multiply the exponents

• Add the exponents

• Subtract the exponents

• Divide the exponents

Multiple Choice

Consider the equation $\left(3^{\frac{x}{2}}\right)\left(3^{\frac{x}{3}}\right)=3^9$  .

Use the Product of Powers property to solve for x.

•  $x\ =\ \frac{54}{5}$  

•  $x=9$ 

•  $x=1$  
  

•  $x=\frac{36}{5}$  
  

Multiple Choice

Consider the equation $\left(2^{\frac{x}{4}}\right)\left(2^{\frac{x}{6}}\right)=2^3$  .

Use the Product of Powers property to solve for x.

•  $x\ =\ 72$  

•  $x=7.2$ 

•  $x=10$  
  

•  $x=2$  
  

That is how we use the Product of Powers Property to solve equations with rational exponents.

Let's see how we can use other properties!

Multiple Choice

 Consider the equation: $27^{\left(x-4\right)}=3^{\left(2x-6\right)}$ 


Which property of exponents does this look like we will use to solve for x?

• Power of a power

• Power of a product

• Product of powers

• Quotient of powers

We need to think about this a little deeper. It doesn't look like a power of a power rule. So we have to make it look like it!

 $27^{\left(x-4\right)}=3^{\left(2x-6\right)}$  

Great work! We are just about finished.

I have one final question as food for thought...

Open Ended

We know that  $2^0=1$  ,  $2^{\left(\frac{1}{2}\right)}=\sqrt{2}$  ,   $2^1=2$  ,  $2^2=4$  , etc. 

What is the value of  $2^{\left(-1\right)}$  ?

Poll

Please rate your current state of understanding of the learning target.

Learning Target: I can solve equations with rational exponents.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there.

• 1 - I don't understand, I need some more help.

Lovely work! Move to Google Classroom and complete your exit ticket.