Rewrite as a cube: 64; −216; 0.008; 1/64; 4 17/27

64 = 4³

-216 = (-6)³

.008 = 0.2³ . . . . . . 1000 = 10³, 8 = 2³. This is 8/1000, so the cube of 2/10

1/64 = (1/4)³ . . . . . . the inverse of the first number

4 17/27 = 125/27 = (5/3)³

You can see that it would be helpful to have memorized the cubes of small integers.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)