This time i has multiple questions.

Question

-(5)^-1
(the test reset and i forgot the answer)

Suppose a spherical asteroid has a radius of approximately 3.2 x 10^3 m.
use the formula 4/3 pi r^3 to find the approximate volume of the asteroid.
This one is straight up confusing, so plz help.

What is the simplifyed form of the following expression?
(y^-5)^-10y^10
I think this one is y^150. Am i wrong or correct?
last one (for now) is

Radio signals at a rate of 3 x 10^8 meters per second. How many seconds would it take for a radio signal to travel from a satellite to the surface of the earth if the satellite is orbiting at a height of 4.2 x 10^7 meters? (hint time is distance divided by rate)
A: 1.26 x 10^16
B: 1.26 x 10^15*******
C: 1.4 x 10^1
D: 1.4 x 10^-1
Am i correct
Please help i has a b- in algebra and i really suck at this unit (Exponents and exponential functions) and i really don't wanna fail this test. I'm so close to straight A's.

Answer 1

-(5)^-1 = -1/5^1 = -1/5

how is the asteroid confusing? You even have the formula.
v = 4/3 πr^3
So, using your value for r, that gives you
4/3 π (3.2 x 10^3)^3 = 4/3 π * 3.2^3 x 10^9 = 137.26 x 10^9 = 1.37 x 10^11

verb: simplify
participle: simplified
(y^-5)^-10 y^10 = y^(-5 * -10) y^10 = y^50 y^10 = y^60
y^150 would be (y^-5 * y^-10)^-10

Huh? They even told you that time = distance/speed
(4.2 x 10^7) / (3 x 10^8) = (4.2/3) x 10^(7-8) = 1.4 x 10^-1
You must have multiplied. And always do a sanity check.
Do you really think it takes 38 million years for the signal to reach earth?