Question

Trevor is tiling his bathroom floor, which has an area that is represented as 120r3 square inches. Each tile has an area of square root of the quantity 16 r to the ninth power. The total number of tiles used can be represented by the expression below.
one hundred twenty r to the third power, all over the square root of the quantity sixteen r to the ninth power

Simplify the expression for the total number of tiles used. Show your work.

@Nurali @zepdrix

Answer 1

\[\Large A=120r^3 \qquad\text{Total Area}\]\[\Large a=16r^9 \qquad\text{Area of each tile}\]
\[\Large n=\frac{A}{a} \qquad\text{Number of tiles}\]
\[\Large n=\frac{120r^3}{16r^9}\]
So let's divide the constants and the r's separately.\[\Large n=\frac{120}{16}\cdot\frac{r^3}{r^9}\]What does the division of the constants give us?

Answer 2

120/16 = ?

Answer 3

One moment please, I have to write all of this on a program, and it takes a bit of time.

Answer 4

Oh I see :) lol

Answer 5

Like this: http://www.sketchtoy.com/48555621 and 120/16 is 7.5

Answer 6

\[\Large n=7.5\cdot\frac{r^3}{r^9}\]Ok good.
To divide exponentials of the same base, we `subtract` the exponents.

Example:\[\Large \frac{x^\color{green}{2}}{x^\color{royalblue}{5}}=x^{\color{green}{2}-\color{royalblue}{5}}=x^{-3}\]

Answer 7

http://www.sketchtoy.com/48555862

Answer 8

@zepdrix x^-6

Answer 9

r^-6 for our problem? Yay good job :)

Answer 10

Is that all @zepdrix ?

Answer 11

\[\Large n=7.5r^{-6}\]Yes.
You could rewrite it as Nurali did to make it look a bit prettier,\[\Large n=\frac{15}{2r^6}\]But it's no big deal :)

Answer 12

How did Nurali get that? o.o

Answer 13

\[\Large 7.5\cdot\frac{2}{2}=\frac{15}{2}\]That was to deal with the decimal.

Answer 14

Oh, okay.

Answer 15

For the other part, you need to recall a rule of exponents.
We can switch the sign on the exponent by tossing it into the denominator.\[\Large r^{-6}=\frac{1}{r^6}\]

Answer 16

Thanks again! ^_^

Answer 17

yay team \c:/