What about
Other Bases?
Lesson 6
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2019 Open Up Resources |
Let’s explore exponent patterns with bases other than 10!
Today’s Goal
True or False:
Comparing Expressions with Exponents
Warm Up
Is each statement true or false?
Be prepared to explain your reasoning.
(-5)2 > -52
(-3)3 = 33
(-3)2 < 32
35 < 46
What Happens with Zero and Negative Exponents?
Activity 1
Begin working on your own.�
Then share your reasoning with �your team after completing �the problem.
Look for similarities to
work we’ve done with base 10!
How does 10−3 compare to 2−3?
Are you ready for more?
Exponent Rules with
Bases Other than 10
Activity 2
Take turns selecting an expression, determining whether the expression matches the original, and explaining your reasoning.
(10 minutes of work time)
not equivalent
not equivalent
not equivalent
not equivalent
What mistakes might lead to the expressions that are not equivalent to the original expression?
We saw before that 103 shows repeated multiplication 10•10•10 and 10-3 shows the repeated multiplication 1/10•1/10•1/10.
How do 23 and 2-3 compare to 103 and 10-3?
The repeated multiplication works the same way!
23 = 2 • 2 • 2 2-3 = ½ • ½ • ½
How do 53 and 5-3 compare to 103 and 10-3?
The repeated multiplication works the same way!
53 = 5 • 5 • 5 5-3 = ⅕ • ⅕ • ⅕
How is (-3)4 different than -34?
(-3)4 = (-3)(-3)(-3)(-3)
-34 = -(3 • 3 • 3 • 3)
Do the other exponent rules work the same way that they did for base 10?
Give some examples with different bases.
What about combining bases?
Do you agree that 35 • 43 = 128?
No, you cannot combine bases in this way.
(3•3•3•3•3) • (4•4•4) ≠ 128
Big Idea
Exponent rules with other bases work exactly the same way as they did with 10.
Today’s Goal
Spot the Mistake
Cool Down