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lisov135 [29]
3 years ago
9

Mr. Stevenson is ordering shirts and hats for his Boy Scout troop. There are 45 scouts in the troop. Hats come in packs of 3, an

d shirts come in packs of 5. What is the least number of packs of each he should order so that each scout will have 1 hat and 1 shirt, and none will be left over?
Mathematics
1 answer:
luda_lava [24]3 years ago
5 0
9 packs of shirts 15 packs of hats
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Drag values to complete each equation.
Alex777 [14]

Answer:

1. A. 1

2. D. 17^9

Step-by-step explanation:

Properties used:

  • Power of a Power Property
  • Product Property
  • Quotient Property
  • Zero Exponent Property

1. First, let's deal with the numerator.

(17^3)^6 can be turned into 17^1^8 by using the Power of a Power Property.

And then use the Product Property, (17^1^8)(17^-^1^0) = 17^8

So now, our fraction is this: \frac{17^8}{17^8}

All number over itself in a fraction is equal to 1. But you can also do this the mathmatic way using the Quotient Property: \frac{a^m}{a^n} = a^m^-^n or \frac{1}{a^(^n^-^m^)}. Which then you plug the numbers in: \frac{17^8}{17^8} = 17^8^-^8 = 17^0. And since we know that in Zero Exponent Property: a^0 = 1, we can see that 17^0 = 1. So either way, we get 1.

So the answer is 1, which is A

2. Power of a Power Property: (a^m)^n = a^m^n

So plug the numbers in the property: (17^{6}) ^3= 17^1^8

Product Property: (a^m)(a^n) = a^m^+^n

We plug the equation in with (17^{6}) ^3 turned into 17^1^8 ---

(17^1^8)(17^-^9) = 17^1^8^-^9 = 17^9

So the answer is 17^9, which is D

I hope this helps!
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