Section 7.3 Rational Exponents

Section 7.3Rational Exponents

Algebra 1

Day 1: Learning Targets• Define a rational exponent.• Define square roots and radical form.• Define and apply the nth root.• Evaluate nth

root expressions.

Rational ExponentsRational exponents are exponents that contain fractions. We can also rewrite them using radicals! Try finding the patterns below…use your calculator to evaluate the following!

What do you notice???

Square Root Definition

Practice converting back and forth between exponential form and radical form. Use the formula above to help you!

Square Root DefinitionWhat is another way we can think about this?

Recall Exponents:42 = 44

Remember, this is saying that I want to multiply the base number out 2 times or write out the

expression using 2 pieces!

What if we had something that looks like this…

Now we know what our answer is from the last slide. However think about what we said to the left. This is asking us to split 16 up into 2 equal pieces…but we

only want 1 out of the 2. Hence the term ROOT when you write it as a radical!

How can I break 16 down into 2 equal pieces? ___ ● ___4 4

2√16𝑜𝑟 1612

Try some on your own!#1:What is ?

Thus,

# 2:Find (or ___)

Thus,

10012

We can also use this same logic for some other problems too!

8114

What if I have something like…

This is now saying that I know 81 can be written as 4 equal pieces and I only want 1 of those 4 pieces.

How can I break 81 down into 4 equal pieces? ___ ● ___ ● ___ ● ___

What would my answer by if I want only 1 out of those 4? ____

Practice with Roots#1) What is ?

Thus,

#2) Find (or ___)

Thus,

3215

What have we been doing every time to rewrite the expression from radical form to exponential form?

Root Definition

𝑏1𝑛=𝑛√𝑏

#3) What is ? #4) Find

Use the same logic for advanced roots too!

1634

What if I have something like…

This is now saying that I know 16 can be written as 4 equal pieces and I want 3 of those

4 pieces.

How can I break 16 down into 4 equal pieces? ___ ● ___ ● ___ ● ___

What would my answer by if I want 3 out of those 4? ___ ● ___ ● ___ = ___

Advanced Root Definition

#1) What is ?

Thus,

#2) Find

Thus,

Try some on your own!Practice 3:What is ?

Practice 4:Find

How do you feel?Heads down, thumbs up!

Got it!

Ehh…so, so.

HELP!!!

End of LessonKAHOOT!

You MUST fill out the exit ticket along with the kahoot to receive participation points for today’s classwork.

Put the exit ticket in the folder that best rates your current understanding of Lesson 7.3!

HOMEWORK – Day 1 Portion of the Worksheet!

Day 2: Learning Targets• I can solve exponential equations by recognizing how to rewrite expressions in exponential form.

What would x be in the following problems?

We Do: You Do:

Solving Exponential EquationsPower Property of Equality

For any real number and , then if and only if .

Example 1: If , then Example 2: If then

Solving Exponential EquationsPractice 1:Solve

Thus,

Practice 2:Solve

Thus,

2 1

Solving Exponential EquationsPractice #3:Solve

Practice #4:Solve

HomeworkDay 2 Portion of the WorksheetUse your time wisely in class because you will

also be getting a quiz review worksheet to take home!