Math: Algebra I
Laws of Exponents
Objectives
Students will be able to:
• State the laws of exponents.
• Simplify expressions with exponents.
Warm-Up
Calculate the following:
• 32
• (4 + 1L2
• 23
Lesson
• Introduction:
We know that 32 = 9 and 33 = 27. What is 33 μ 32 ?
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Math: Algebra I Laws of Exponents
í Suppose you know that 36 = 729. To find 33 μ 33 , is there an easier way than multiplying 27 and
27?
í What about 33 ë 32 ?
í Or I33 M ?
2
Math: Algebra I Laws of Exponents
• Student exploration: Try to write the laws of exponents by exploring this concept through
Wolfram|Alpha.
Assume a > 0.
í What is Iax M Iay )?
í What is Iax M ë Iay )?
í How about Iax M ?
y
Have students try different examples in Wolfram|Alpha to see if they can figure out the laws of
exponents on their own.
3
4
Math: Algebra I Laws of Exponents
Math: Algebra I Laws of Exponents
• Regroup your students as a class and take volunteers for each of the above questions. Once your
students have shared their ideas, solidify these concepts with the actual laws and an example of
each.
í ax ay = ax+y
For example, simplify: b4 b2
y
í Iax M = ax y
For example, simplify: I72 M
í
ax
ay
4
= aHx-yL
For example, simplify:
z4
z8
(assuming z ∫ 0)
í a1 = a
í a0 = 1 (assuming a ∫ 0)
Closing
Answer the following and have the answer checked before your students leave to demonstrate
understanding of the concept.
Simplify :
I24 M
7
25
Demonstrations
Exponents
Laws of Exponents
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