Answer:
Simplified base would be 3∛4
Step-by-step explanation:
Given exponential function,
![f(x)=\frac{1}{4}(\sqrt[3]{108})^x](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B4%7D%28%5Csqrt%5B3%5D%7B108%7D%29%5Ex)
Since, in an exponential function 
b is called base.
∵ 108 = 2 × 2 × 3 × 3 × 3,
Or 108 = 4 × 3³,
![\implies \sqrt[3]{108} = \sqrt[3]{4\times 3^3}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%5B3%5D%7B108%7D%20%3D%20%5Csqrt%5B3%5D%7B4%5Ctimes%203%5E3%7D)
![\sqrt[3]{108}=\sqrt[3]{4}\times \sqrt[3](3^3)](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B108%7D%3D%5Csqrt%5B3%5D%7B4%7D%5Ctimes%20%5Csqrt%5B3%5D%283%5E3%29)
( Using ![\sqrt[n]{ab}=\sqrt[n]{a}\times \sqrt[n]{b}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5Ctimes%20%5Csqrt%5Bn%5D%7Bb%7D)
)
![\sqrt[3]{108}=\sqrt[3]{4}\times (3^3)^\frac{1}{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B108%7D%3D%5Csqrt%5B3%5D%7B4%7D%5Ctimes%20%283%5E3%29%5E%5Cfrac%7B1%7D%7B3%7D)
![\sqrt[3]{108}=\sqrt[3]{4}\times 3^{3\times \frac{1}{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B108%7D%3D%5Csqrt%5B3%5D%7B4%7D%5Ctimes%203%5E%7B3%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%7D)
( Using power of power property of exponent )
![\sqrt[3]{108}=3\sqrt[3]{4}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B108%7D%3D3%5Csqrt%5B3%5D%7B4%7D)
Hence, the required simplified base would be 3∛4
i.e. SECOND option is correct.
The correct answer is 3/20
Hope this helped :)
Y= 5
5(8) - 2(5)
40 - 10 = 30
Answer:
An actual distance of 360 miles correspond to 9 inches on the map
Step-by-step explanation:
From the question, we have a scale of 0.5 inches representing 20 miles
Now, we want to relate an actual distance of 360 miles to a measurement on the map using the scale
From here, we have that;
0.5 inches = 20 miles
x inches = 360 miles
x * 20 = 0.5 * 360
20x = 180
x = 180/20
x = 9 inches
