Work in pairs to figure out a rule for each of the following situations. Try out different numeric examples to find a pattern. Use a=2, b=7, m=3, and n=5 for your first example, then choose your own numbers for the other two. Once you have a conjecture for what the rule is, try proving it to yourselves by using non-exponential notation (or think of a different way to show it!). Use colors and highlighters to show connections and make your work more clear.
Situation
. / - ∙-
(-.)/ (-I). J-K.
-. -/
Numeric Examples
2# ∙ 20 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 = 22 = 256
1 ' 1 # 1 1 1 1 1 1 0 10 1 C4E ∙C4E =4∙4∙4∙4∙4=C4E =40 =1024
10' ∙10"' =10∙10∙ 1 ∙ 1 =1=10* 10 10
Rule Conjecture
Demonstration