Question

Compute \dfrac{(2/3)^3}{(2/9)^2}.

Answer 1

\[ \dfrac{(\frac{2}{3})^3}{(\frac{2}{9})^2} = \frac{\frac{2^3}{3^3}}{\frac{2^2}{9^2}}\]

you should multiply top and bottom by the reciprocal of the bottom fraction
9^2/2^2
can you do that ?

Answer 2

ok

Answer 3

I would not multiply anything, just write down the reciprocal times the top and bottom

Answer 4

it will look like this
\[ \frac{\frac{2^3}{3^3}\cdot \frac{9^2}{2^2}}{\frac{2^2}{9^2} \cdot \frac{9^2}{2^2}} \]

Answer 5

notice in the bottom of that mess, the 2^2 in the top divided by 2^2 in the bottom
and the 9^2 is divided by 9^2. In other words the bottom is 1
\[ \frac{\frac{2^3}{3^3}\cdot \frac{9^2}{2^2}}{\frac{2^2}{9^2} \cdot \frac{9^2}{2^2}} = \frac{\frac{2^3}{3^3}\cdot \frac{9^2}{2^2}}{1}\]

does that part make any sense?

Answer 6

yep

Answer 7

dividing by 1 can be ignored: example 3/1 is 3 or 10/1 is 10, and so on. So we have
\[ \frac{2^3}{3^3}\cdot \frac{9^2}{2^2} \]

Answer 8

now let's do the twos

2^3 / 2^2

any idea?

Answer 9

2

Answer 10

so now we have
\[ \frac{2 \cdot 9^2}{3^3} \]

Answer 11

ok

Answer 12

remember what those little numbers in the upper right mean: multiply by itself
so we could do this
\[ \frac{ 2 \cdot 9 \cdot 9}{ 3 \cdot 3 \cdot 3} \]
can you simplify that ?

Answer 13

yes

Answer 14

what do you get?

Answer 15

6

Answer 16

yes.

Answer 17

another way to think of it is
\[ \frac{2 \cdot 9^2}{3\cdot 3^2} = \frac{2}{3}\cdot \left(\frac{9}{3}\right)^2 = \frac{2}{3}\cdot 3^2 = 2 \frac{3^2}{3} = 2 \cdot 3 = 6\]

Answer 18

oh

Answer 19

another way is write 9 as 3^2
\[ \frac{2 \cdot 9^2}{3^3} = \frac{2 \cdot \left(3^2\right)^2}{3^3} =
\frac{2 \cdot 3^4}{3^3} = 2\cdot \frac{3^4}{3^3} = 2\cdot3=6\]

Answer 20

ok

Answer 21

hopefully some of that makes sense. But it should!

Answer 22

oh, ok Thanks so much I'm going to be a fan.

Answer 23

ty

Answer 24

and though you should only do this as a check, the easiest way to solve is type into the google search window
(2/3)^3 / (2/9)^2=