64 Rational Exponents - MRS. GUERRIERO€¦ · 64 Rational Exponents Square Roots A square root is...
Transcript of 64 Rational Exponents - MRS. GUERRIERO€¦ · 64 Rational Exponents Square Roots A square root is...
1
Lesson Objectives Teacher's Notes Lesson Notes
64 Rational Exponents
Square Roots
A square root is equivalent to an exponent of onehalf.
exponent___________________________
index2 1
Why? _________________________________
Erase the blue oval to check your explanation.
2
Cube roots
What exponent is equivalent to a cube root?
311 exponent
___________________________
index
Converting Practice
Write using rational exponents.
Press tiles to reveal solutions.
3
nth RootsWhat exponent is equivalent to an nth root?
Use the magnifying glass to reveal the answer.
mn__
Pull for Teacher's Notes
Some students may benefit from a summary of the general rule:
• The index becomesthe denominator.
• The exponent becomes
the numerator.
Reducing Practice
Write using rational exponents. Then reduce.
Press tiles to reveal solutions.
4
Number Cube Practice
Use number cubes to generate values of m and n. Write as a rational exponent. Reduce if necessary.
n:
m:
Pull for Teacher's Notes
Help students realize that m becomes the numerator of the rational exponent.
Likewise, n becomes the denominator of the rational exponent.
Have students reduce the rational exponent they get.
Convert and simplify numerically and check with your calculator.
5
Match Equivalents
Pull for Teacher's Notes
Some expressions are complicated and challenging.
Have students look for expressions that are obviously equivalent.
Click on the snap button when the expressions shown on the cards are equivalent.
ChallengeWrite these rational exponents using radicals. Then click each tile to check your answers.
6
Fire up those clickers ...
1 What is the index of a square root?A
B
C
D 2
7
2 Which exponent is equivalent to a square root?
A
B
C
D
3 Which exponent is equivalent to a cube root?
A
B
C
D
8
4 What is written using rational exponents?
A
D
B
C
5 What is written using rational exponents?
A
D
B
C
9
6 What is written using rational exponents?
A
D
B
C
7 What is written using rational exponents?
A
D
B
C
10
8 How do you reduce a rational exponent?
A Cancel common factors in the numerator and denominator.
B Subtract common factors in the numerator and denominator.
C Take the square root of common factors in the numerator and denominator.
D Subtract the square root of common factors in the numerator and denominator.
9
A
D
B
C