Answer:

Step-by-step explanation:
We are given an expression and we have to transform it into an expression with exponent.
5th root of x can be written as 
![(\sqrt[5]{x^7})^3\\\\((x^7)^\frac{1}{5} )^3](https://tex.z-dn.net/?f=%28%5Csqrt%5B5%5D%7Bx%5E7%7D%29%5E3%5C%5C%5C%5C%28%28x%5E7%29%5E%5Cfrac%7B1%7D%7B5%7D%20%29%5E3)
The powers outside will be multiplied as: 

where the exponent is
and it is a rational number by definition of rational numbers
Answer:
>
Step-by-step explanation:
5 is greater than the
.
= 4.24264068712
...
<u>Hope this helps and have a nice day!</u>
Answer:
y-intercept: 10
concavity: function opens up
min/max: min
Step-by-step explanation:
1.) The definition of a y-intercept is what the resulting value of a function is when x is equal to 0.
Therefore, if the function's equation is given, to find y-intercept simply plug in 0 for the x-values:

y intercept ( f(0) )= 10
2.) In order to find concavity (whether a function opens up or down) of a quadratic function, you can simply find the sign associated with the x^2 value. Since 2x^2 is positive, the concavity is positive. This is basically possible, since it is identifying any reflections affecting the y-values / horizontal reflections.
3.) In order to find whether a quadratic function has a maximum or minimum, you can use the concavity of the function. The idea is that if the function opens downwards, the vertex would be at the very top, resulting in a maximum. If a function was open upwards, the vertex would be at the very bottom, meaning there is a minimum. Like the concavity, if the value associated with x^2 is positive, there is a minimum. If it is negative, there is a maximum. Since 2x^2 is positive, the function has a minimum.
Answer:Lateral surface area is 847.8 centimeters^2
Step-by-step explanation:
The formula for determining the lateral surface area of a cylinder is expressed as
Lateral surface area = 2πrh
Where
r = radius of the cylinder
h = the height of the cylinder
From the information given,
r = 9 centimeters
h = 15 centimeters
π = 3.14
Lateral surface area = 2 × 3.14 × 9 × 15 = 847.8 centimeters^2