Answer:
1. A. 1
2. D. [tex]17^9[/tex]
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.
[tex](17^3)^6[/tex] can be turned into [tex]17^1^8[/tex] by using the Power of a Power Property.
And then use the Product Property, [tex](17^1^8)(17^-^1^0) = 17^8[/tex]
So now, our fraction is this: [tex]\frac{17^8}{17^8}[/tex]
All number over itself in a fraction is equal to 1. But you can also do this the mathmatic way using the Quotient Property: [tex]\frac{a^m}{a^n} = a^m^-^n[/tex] or [tex]\frac{1}{a^(^n^-^m^)}[/tex]. Which then you plug the numbers in: [tex]\frac{17^8}{17^8} = 17^8^-^8 = 17^0[/tex]. And since we know that in Zero Exponent Property: [tex]a^0 = 1[/tex], we can see that [tex]17^0 = 1[/tex]. So either way, we get 1.
So the answer is 1, which is A
2. Power of a Power Property: [tex](a^m)^n = a^m^n[/tex]
So plug the numbers in the property: [tex](17^{6}) ^3[/tex]= [tex]17^1^8[/tex]
Product Property: [tex](a^m)(a^n) = a^m^+^n[/tex]
We plug the equation in with [tex](17^{6}) ^3[/tex] turned into [tex]17^1^8[/tex] ---
[tex](17^1^8)(17^-^9) = 17^1^8^-^9 = 17^9[/tex]
So the answer is [tex]17^9[/tex], which is D
I hope this helps!
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