Question

A glass cylinder is completely filled with 32m6n2 cubic inches of salt solution. The jug has a base area of 8m3n2 square inches. The height of the jug, in inches, is represented by the expression The quantity of 32 m to the sixth n squared all over 8 m cubed n squared.

Which of the following simplified expressions represents the height of the jug in inches?

4m9n4

4m2n

4m2

4m3

Answer 1

Volume = (Area of base)*(height)

Answer 2

wait a second...are there 2 figures? A cylinder and a jug?

Answer 3

idk I'm guessing it's just one.

Answer 4

oh i see now, nvm

Answer 5

they're saying

" The height of the jug, in inches, is represented by the expression The quantity of 32 m to the sixth n squared all over 8 m cubed n squared."

so..

\[\Large h = \frac{32m^6n^2}{8m^3n^2}\]

Answer 6

reduce that fraction to get your answer

Answer 7

can you reduce it for me please?

Answer 8

let's break it up

Answer 9

32/8 = ???

Answer 10

4

Answer 11

m^6 divided by m^3 = ???


(subtract the exponents when dividing expressions like this with the same base)

Answer 12

m3

Answer 13

m^3, yep

Answer 14

n^2 divided by n^2 = ???

Answer 15

it would be 0 so the n wouldn't be there anymore

Answer 16

we'd get n^0

Answer 17

so,

\[\Large h = \frac{32m^6n^2}{8m^3n^2}\]
\[\Large h = 4m^3n^0\]
\[\Large h = 4m^3*1\]
\[\Large h = 4m^3\]

Answer 18

keep in mind that anything to the 0th power is 1 (except 0 itself)

so, \[\Large n^0 = 1\]

Answer 19

so the final answer is \[4m^{3}\]

Answer 20

?

Answer 21

correct

Answer 22

thank you :)

Answer 23

you're welcome