Answer:
Here we will use the relationships:
![a^n*a^m = a^{n + m}](https://tex.z-dn.net/?f=a%5En%2Aa%5Em%20%3D%20a%5E%7Bn%20%2B%20m%7D)
![(a^n)^m = a^{n*m}](https://tex.z-dn.net/?f=%28a%5En%29%5Em%20%3D%20a%5E%7Bn%2Am%7D)
![\frac{a^n}{a^m} = a^{n - m}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5En%7D%7Ba%5Em%7D%20%3D%20a%5E%7Bn%20-%20m%7D)
And a number:
![a^n](https://tex.z-dn.net/?f=a%5En)
is between 0 and 1 if a is positive and larger than 1, and n is negative.
if a is positive and 0 < a < 1, then we need to have n positive such that:
0 < a^n < 1
A) ![5^3*5^{-4} = 5^{3 + (-4)} = 5^{-1}](https://tex.z-dn.net/?f=5%5E3%2A5%5E%7B-4%7D%20%3D%205%5E%7B3%20%2B%20%28-4%29%7D%20%3D%205%5E%7B-1%7D)
This is between zero and 1,
B) ![\frac{3^5}{3^{-6}} = 3^{5 - (-6)} = 3^{11}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E5%7D%7B3%5E%7B-6%7D%7D%20%3D%203%5E%7B5%20-%20%28-6%29%7D%20%3D%203%5E%7B11%7D)
This is greater than 1, because the exponent is positive.
C) ![(\frac{1}{4})^3*( \frac{1}{4})^2 = (\frac{1}{4})^{2 + 3} = (\frac{1}{4})^5](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%29%5E3%2A%28%20%5Cfrac%7B1%7D%7B4%7D%29%5E2%20%3D%20%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%20%2B%203%7D%20%3D%20%28%5Cfrac%7B1%7D%7B4%7D%29%5E5)
Because a is smaller than 1, and the exponent is positive, then the expression is between 0 and 1.
D) ![\frac{(-7)^5}{(-7)^7} = (-7)^{5 - 7} = -7^{-2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28-7%29%5E5%7D%7B%28-7%29%5E7%7D%20%3D%20%28-7%29%5E%7B5%20-%207%7D%20%3D%20-7%5E%7B-2%7D)
The exponent is negative (and pair) then the expression is between 0 and 1.
Remember that when the exponent is pair, we always have that:
(-N)^m = (N)^m
So (-7)^-2 = 7^-2
Answer:
x= 102 degrees
Step-by-step explanation:
It is an isosceles triangle, which means that it has two equal sides and angles, so the angles opposite of 3.3 are going to be the same or 39 degrees, which means, 39 + 39 is 78 and 180 - 78 is 102 and x=102 degrees.
Answer:
B. (0,0)
Step-by-step explanation:
The y-intercept of the equation f(x) = 1/2x lies on the y-axis.
This means we need to set x = 0 and solve for y
1/2(0) = 0
Therefore, (0,0) is the y-intercept of this equation.
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