Simplify ^3√135 3^3√5 5^3√5 27^3√5 25^3√3

∛135 = 3∛5

∛135 = ∛(27×5) = ∛27 × ∛5 = 3∛5

As with any root, the root of a product is the product of the roots of the factors. Here, the only cubic factor is 27 = 3³.

Comment on powers and roots

It can help immensely if you are familiar with the squares and cubes of small integers. Of course, your knowledge of regular times tables will get you to the fact that ...

... 27 = 3·9 = 3·3·3 = 3³

Knowledge of divisibility rules is helpful, too. Here, you can see that 135 ends in 5, so you know that 5 is a factor of the number.

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3