Answer:
8. Louis
9. Rose; Raymond
Step-by-step explanation:
8. An exponent represents the number of times the base appears as a factor in the product.
We use a coefficient to signify repeated addition: 3x means x+x+x.
We use an exponent to signify repeated multiplication. x³ means x·x·x.
So, the expression ...
You can see that the factor 4 appears 7 times in the product, so would be represented in exponential form as ...
Louis has correctly observed this fact. In general, we see that multiplying powers of the same base causes those powers to be added.
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9.
<u>Part A</u>. Rose is correct for the same reason as in problem 8.
5^5 · 5^2 = 5^(5+2) = 5^7
<u>Part B</u>. Raymond is correct. We know that division cancels similar terms from the numerator, so ...
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The rules of exponents we're using here are ...
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)