Question

Drag values to complete each equation.

Answer 1

Answer:

1. A. 1

2. D. 17^9

Step-by-step explanation:

Answer 2

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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