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Alexus [3.1K]
3 years ago
15

Someone please help me

Mathematics
1 answer:
aliina [53]3 years ago
4 0

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 ...

  4^2\cdot 4^5\text{  means  }(4\cdot4)\cdot(4\cdot4\cdot4\cdot4\cdot4)

You can see that the factor 4 appears 7 times in the product, so would be represented in exponential form as ...

  4^2\cdot4^5=\boxed{4^7}

Louis has correctly observed this fact. In general, we see that multiplying powers of the same base causes those powers to be added.

__

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 ...

  \dfrac{7^9}{7^5}=\dfrac{7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot7}{7\cdot7\cdot7\cdot7\cdot7}=7\cdot7\cdot7\cdot7=7^{9-5}=7^4

__

The rules of exponents we're using here are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)

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