Question

70 POINTS!!!!!!!!!!!!!! HELP PLEASE

1. Apply the properties of integer exponents to write equivalent numerical expressions. Show all work.
Ex. 32 • 3-5 = 3-3 =

a. 4^1 • 4^2

b. 5^3 • 5^-6


c. 32 • 31

d. 6^5 • 5^-7





2. Select two of the above expressions (one multiplication and one division) and explain how you simplified them.

Answer 1

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Explanation:

When bases are same in multiplication, add exponents.

1) a. 4^1 × 4^2

4^(1+2)

4^3

b. 5^3 × 5^-6

5^(3+-6)

5^(-3)

c. 3^2 × 3^1

3^(2+1)

3^3

d. 6^5 × 5^-7

0.0995328

2. I added the exponents. For the last one, I evaluated by calculator.

Answer 2

4^1 * 4^2 = 4^(1 + 2) = 4^3 = 64

5^3 * 5^-6 = 5^(3 - 6) = 5^-3 = 1/125

The third one down is rather sneaky. It's also kinda neat.
31 = 32 - 1 = 2^5 - 1
32 * 31
= 32 (2^5 - 1)
= 2^5(2^5 - 1)
= 2^10 - 2^5
= 1024 - 32
= 992

I don't see any math tricks to solve this. Use brute force.
6^5 * 5^-7 = 6^5 / 5^7 = 7776 / 17125 = 0.00953

2. Just pick a couple of questions out of the four above. The last one is a good example for division. The first one would be good for multiplication. I've explained all you need.