Answer:
![(4^{-2})^5=\dfrac{1}{4^{10}}](https://tex.z-dn.net/?f=%284%5E%7B-2%7D%29%5E5%3D%5Cdfrac%7B1%7D%7B4%5E%7B10%7D%7D)
Step-by-step explanation:
The given expression is : ![(4^{-2})^5](https://tex.z-dn.net/?f=%284%5E%7B-2%7D%29%5E5)
We need to simplify the above expression.
We know that, ![x^{-a}=\dfrac{1}{x^a}](https://tex.z-dn.net/?f=x%5E%7B-a%7D%3D%5Cdfrac%7B1%7D%7Bx%5Ea%7D)
or
![(4^{-2})^5=(\dfrac{1}{4^2})^5\\\\=\dfrac{1^5}{(4^2)^5}\\\\\because (x^b)^c=x^{b\times c}\\\\=\dfrac{1}{4^{10}}](https://tex.z-dn.net/?f=%284%5E%7B-2%7D%29%5E5%3D%28%5Cdfrac%7B1%7D%7B4%5E2%7D%29%5E5%5C%5C%5C%5C%3D%5Cdfrac%7B1%5E5%7D%7B%284%5E2%29%5E5%7D%5C%5C%5C%5C%5Cbecause%20%28x%5Eb%29%5Ec%3Dx%5E%7Bb%5Ctimes%20c%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B4%5E%7B10%7D%7D)
So, the simplified form of the given expression is
. Hence, the correct option is (A).
- Zero Product Property: if a × b = 0, then either a or b = 0 or both a and b = 0.
(Make sure to set f(x) to zero)
So for this equation, I will be factoring by grouping. Firstly, what two terms have a product of -5x^2 and a sum of 4x? That would be 5x and -x. Replace 4x with 5x - x: ![0=5x^2+5x-x-1](https://tex.z-dn.net/?f=0%3D5x%5E2%2B5x-x-1)
Next, factor 5x^2 + 5x and -x - 1 separately. Make sure that they have the same quantity on the inside: ![0=5x(x+1)-1(x+1)](https://tex.z-dn.net/?f=0%3D5x%28x%2B1%29-1%28x%2B1%29)
Now you can rewrite the equation as: ![0=(5x-1)(x+1)](https://tex.z-dn.net/?f=0%3D%285x-1%29%28x%2B1%29)
Now apply zero product property to the factors to solve for x:
![5x-1=0\\5x=1\\x=\frac{1}{5}\\\\x+1=0\\x=-1](https://tex.z-dn.net/?f=5x-1%3D0%5C%5C5x%3D1%5C%5Cx%3D%5Cfrac%7B1%7D%7B5%7D%5C%5C%5C%5Cx%2B1%3D0%5C%5Cx%3D-1)
<u>The x-intercepts are (1/5 ,0) and (-1,0).</u>
its the first 1. b.
Step-by-step explanation:
nb. b. b b b bcbcbc