Properties of Exponents: IM Alg2.3.1
[url=https://im.kendallhunt.com/HS/teachers/3/3/1/preparation.html]“Properties of Exponents”[/url] from IM Algebra II © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg2.3.1 Lesson
- IM Alg2.3.1 Lesson: Properties of Exponents
- Alg2.3.1 Practice
- IM Alg2.3.1 Practice: Properties of Exponents
IM Alg2.3.1 Lesson: Properties of Exponents
Which one doesn’t belong?
A. [math]2^3=9[/math][br]B. [math]9=3^2[/math][br]C. [math]2\cdot2\cdot2\cdot2=16[/math][br]D. [math]a\cdot2^0=a[/math]
Find the value of each variable that makes the equation true. Be prepared to explain your reasoning.
[math]2^3\cdot2^5=2^a[/math]
[math]3^b\cdot3^7=3^{11}[/math]
[math]\frac{4^3}{4^2}=4^c[/math]
[math]\frac{5^8}{5^d}=5^2[/math]
[math]6^m\cdot6^m\cdot6^m=6^{21}[/math]
[math](7^n)^4=7^{20}[/math]
[math]2^4\cdot3^4=6^s[/math]
[math]5^3\cdot t^3=50^3[/math]
Use exponent rules to write each expression as a single power of 2. Find the value of the expression. Record these in the table. The first row is done for you.
What is the value of [math]5^0[/math]?[br]
What is the value of [math]3^{-1}?[/math]
What is the value of [math]7^{-3}[/math]?[br]
Explain why the argument used to assign a value to the expression [math]2^0[/math] does not apply to make sense of the expression [math]0^0[/math].
Sort expressions that are equal into groups. Some expressions may not have a match, and some may have more than one match. Be prepared to explain your reasoning.
IM Alg2.3.1 Practice: Properties of Exponents
Find the value of each variable that makes the equation true.
[math]2^5\cdot2^3=2^a[/math][br][br]
[math]\frac{7^4}{7^b}=7^{\text{-}2}[/math]
[math]8^c=\frac{1}{64}[/math]
[size=150] Select [b]all[/b] the expressions equivalent to [math]7^{\text{-}2}\cdot7^5\cdot7^{\text{-}3}[/math].[/size]
Which expression is equal to [math]\frac{3^8}{3^2}[/math]?
Find the value of each variable that makes the equation true.
[math]\frac{5^6}{5^m}=5^9[/math]
[math]2^3\cdot4^n=2^{11}[/math]
[math](7^4)^k=7^{\text{-}8}[/math]
[size=150]Evaluate the expression [math]\frac{6^3}{6^3}[/math].[/size][br]
[size=150]Explain how this helps show why [math]6^0=1[/math].[br][/size]