Answer:
![\sqrt[4] {x^3}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%20%7Bx%5E3%7D)
Step-by-step explanation:
At this point, we can transform the square root into a fourth root by squaring the argument, and bring into the other root:
![\sqrt x \cdot \sqrt[4] x =\sqrt [4] {x^2} \cdot \sqrt[4] x = \sqrt[4]{x^2\cdot x} = \sqrt[4] {x^3}](https://tex.z-dn.net/?f=%5Csqrt%20x%20%5Ccdot%20%5Csqrt%5B4%5D%20x%20%3D%5Csqrt%20%5B4%5D%20%7Bx%5E2%7D%20%5Ccdot%20%5Csqrt%5B4%5D%20x%20%3D%20%5Csqrt%5B4%5D%7Bx%5E2%5Ccdot%20x%7D%20%3D%20%5Csqrt%5B4%5D%20%7Bx%5E3%7D)
Alternatively, if you're allowed to use rational exponents, we can convert everything:
![\sqrt x \cdot \sqrt[4] x = x^{\frac12} \cdot x^\frac14 = x^{\frac12 +\frac14}= x^{\frac24 +\frac14}= x^\frac34 = \sqrt[4] {x^3}](https://tex.z-dn.net/?f=%5Csqrt%20x%20%5Ccdot%20%5Csqrt%5B4%5D%20x%20%3D%20x%5E%7B%5Cfrac12%7D%20%5Ccdot%20x%5E%5Cfrac14%20%3D%20x%5E%7B%5Cfrac12%20%2B%5Cfrac14%7D%3D%20x%5E%7B%5Cfrac24%20%2B%5Cfrac14%7D%3D%20x%5E%5Cfrac34%20%3D%20%5Csqrt%5B4%5D%20%7Bx%5E3%7D)
Answer:
The line u and line v have no point of intersection because they are parallel lines
Step-by-step explanation:
The slope of a straight line is given as follows;

The slope of line u is (4 - (-8))/(5 - 9) = -3
The equation for line u is y - 4 = -3*(x - 5)
y = -3·x + 15 + 4 = 19 - 3·x
The slope for line v is (-7 - 2)/(7 - 4) = -3
The equation for the line v is y - 2 = -3*(x - 4)
∴ y = -3x + 12 + 2 = -3x + 14
y = 14 - 3·x
Therefore. line u and line v have the same slope and are therefore parallel and they do not intersect
Answer:
x^3-1
Step-by-step explanation:
f(x)=g(x)-1 since was shifted down 1 unit x^3-1
f(x)=g(x)+1 would have been a shift up of 1 unit x^3+1
f(x)=g(x-1) shifted right 1 unit (x-1)^3
f(x)=g(x+1) shifted left one unit (x+1)^3
Anyways the answer is f(x)=x^3-1