Answer: You have to provide the options in order for people to help.
Step-by-step explanation:
Hello!
To find the y-intercept you put in 0's for x
-2(0) + 4(0) + 1 = 1
The answer is (0, 1)
Hope this helps!
Solve the terms in parentheses first. We'll start on the denominator.
The denominator has an exponent for a fraction that also includes exponents. To multiply exponents within parentheses that are raised to a power, use this rule:
![(x^a)^b = x^{a \cdot b}](https://tex.z-dn.net/?f=%28x%5Ea%29%5Eb%20%3D%20x%5E%7Ba%20%5Ccdot%20b%7D)
Simplify the denominator:
![(\frac{3^4}{7^3} )^2 = \frac{3^8}{7^6}](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%5E4%7D%7B7%5E3%7D%20%29%5E2%20%3D%20%5Cfrac%7B3%5E8%7D%7B7%5E6%7D)
Solve the fractions in the numerator:
![(\frac{3}{5})^5 = \frac{3^5}{5^5}](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%7D%7B5%7D%29%5E5%20%3D%20%5Cfrac%7B3%5E5%7D%7B5%5E5%7D)
![(\frac{9}{7})^2} = \frac{9^2}{7^2}](https://tex.z-dn.net/?f=%28%5Cfrac%7B9%7D%7B7%7D%29%5E2%7D%20%3D%20%5Cfrac%7B9%5E2%7D%7B7%5E2%7D)
The problem should now read:
![\frac{\frac{3^5}{5^5} \cdot \frac{9^2}{7^2}}{\frac{3^8}{7^6}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B3%5E5%7D%7B5%5E5%7D%20%5Ccdot%20%5Cfrac%7B9%5E2%7D%7B7%5E2%7D%7D%7B%5Cfrac%7B3%5E8%7D%7B7%5E6%7D%7D)
There is a denominator in a denominator. We can bring that to the numerator of the overall fraction:
![\frac{\frac{3^5}{5^5} \cdot \frac{9^2}{7^2}}{\frac{3^8}{7^6}} = \frac{\frac{3^5}{5^5} \cdot \frac{9^2}{7^2} \cdot {7^6}}{3^8}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B3%5E5%7D%7B5%5E5%7D%20%5Ccdot%20%5Cfrac%7B9%5E2%7D%7B7%5E2%7D%7D%7B%5Cfrac%7B3%5E8%7D%7B7%5E6%7D%7D%20%3D%20%5Cfrac%7B%5Cfrac%7B3%5E5%7D%7B5%5E5%7D%20%5Ccdot%20%5Cfrac%7B9%5E2%7D%7B7%5E2%7D%20%5Ccdot%20%7B7%5E6%7D%7D%7B3%5E8%7D%7D)
Using a calculator, simplify the numerator:
![\frac{3^5}{5^5} \cdot \frac{9^2}{7^2} \cdot {7^6} = \frac{19683}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E5%7D%7B5%5E5%7D%20%5Ccdot%20%5Cfrac%7B9%5E2%7D%7B7%5E2%7D%20%5Ccdot%20%7B7%5E6%7D%20%3D%20%5Cfrac%7B19683%7D%7B7%7D)
The fraction should now read:
![\frac{\frac{19683}{7}}{3^8}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B19683%7D%7B7%7D%7D%7B3%5E8%7D)
There is a denominator in the numerator. This can be brought down to the overall denominator:
![\frac{\frac{19683}{7}}{3^8} = \frac{19683}{3^8 \cdot 7}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B19683%7D%7B7%7D%7D%7B3%5E8%7D%20%3D%20%5Cfrac%7B19683%7D%7B3%5E8%20%5Ccdot%207%7D)
Factor 19683:
![19683 = 3 \cdot3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 = 3^9](https://tex.z-dn.net/?f=19683%20%3D%203%20%5Ccdot3%20%5Ccdot%203%20%5Ccdot%203%20%5Ccdot%203%20%5Ccdot%203%20%5Ccdot%203%20%5Ccdot%203%20%5Ccdot%203%20%3D%203%5E9)
![\frac{19683}{3^8 \cdot 7} = \frac{3^9}{3^8 \cdot 7}](https://tex.z-dn.net/?f=%5Cfrac%7B19683%7D%7B3%5E8%20%5Ccdot%207%7D%20%3D%20%5Cfrac%7B3%5E9%7D%7B3%5E8%20%5Ccdot%207%7D)
Simplify the exponents:
![\frac{3^9}{3^8} = 3](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E9%7D%7B3%5E8%7D%20%3D%203)
The following fraction will be your answer:
![\boxed{\frac{3}{7}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cfrac%7B3%7D%7B7%7D%7D)