Question

I feel like this question is probably actually really simple, and I am just not understanding it... But I need a little help, please!

It says:
This expression evaluates to an integer. Write the integer in the space below, like this: -14

Then it has these numbers...

3 5/3 (yeah a fraction right here)
------------ (then this line)
3 2/3 (and another fraction here)

There is also a line to the right side of the problem.
Unsure what this line represents...

Could someone explain some of this to me?

Answer 1

So it looks like

\(\Large \frac{3\frac{5}{3}}{3\frac{2}{3}}\) ?

Answer 2

Nope cant be that, that's not an integer...

Answer 3

That is how it looks though!

Answer 4

But with another line vertically next to the problem, to the right of it.

Answer 5

like this | but longer

Answer 6

Hmm, any way you can take a screenshot of it and attach it here?

Answer 7

Yeah gimmie a second!

Answer 8

Ah I see what is being asked. It's the fractions separated and they want it in its simplified integer form. Just simplifying both fractions

Answer 9

Take it away jtug!

Answer 10

Oh now I get it....

Answer 11

Okay, that makes sense kinda... But, I am a bit confused on how to simplify these together for one integer... How should I do this??

Answer 12

Take the denominator multiply it by the whole number to the left then add it to the numerator

Answer 13

No, dont fall into that trap, thats what I thought too...but no these are not mixed numbers, we are dealing with exponents

I had \(\Large \frac{3\frac{5}{3}}{3\frac{2}{3}}\) when it should be \(\Large \frac{3^\frac{5}{3}}{3^\frac{2}{3}}\)

Answer 14

From this, it is important to remember the laws of exponents

\[\large \frac{x^a}{x^b} = x^{a - b}\]

Answer 15

Oh! I didn't look @ the image. Okay so it's an exponent? That makes sense then

Answer 16

My bad thought it was two separate mixed numbers XD

Answer 17

You with us @ghosting ?

Answer 18

Nope, I am long gone!!! @__@ What do I do now.... confuzzled, sorry.

Answer 19

Okay so... those fractions are actually squared by the whole numbers... I get that part.. .__. I think. Right?

Answer 20

Nope dont let it overwhelm you!

Remember an exponent is simply something raised to a power

\(\large 2^4, 6^{10}, 4^{22}\) etc...

So let me take a tangent quick here...

If I gave you \(\Large \frac{2^4}{2^2}\) and told you the law to follow is \(\Large \frac{x^a}{x^b} = x^{a - b}\)

What would you get?

Answer 21

4?

Answer 22

That is the correct answer yes...and you got it by doing

\[\large \frac{2^4}{2^2} = 2^{4 - 2} = 2^2 = 4\]

Right?

Answer 23

Correct!

Answer 24

Good! So back to your problem

\[\large \frac{3^\frac{5}{3}}{3^\frac{2}{3}}\]

Treat it the SAME way..doesn't matter that we are working with fractions this time

Answer 25

I have no idea what to do with the fractions, though. Would I multiply 5/3 3 times? or..

Answer 26

Nope...just like the last problem...you left the big 2 alone right? And only subtracted the exponents (4 - 2)

Here you do the same...leave the big 3 alone...and subtract the exponents

\[\Large \frac{3^\frac{5}{3}}{3^\frac{2}{3}} = 3^{\frac{5}{3} - \frac{2}{3}}\]

So just ask yourself...what is \(\large \frac{5}{3} - \frac{2}{3}\)

Answer 27

We get 1. :D so it's 3^1? so just 3, right?

Answer 28

Exactly! :)

Answer 29

COOL, Wow! Thank you so much for the help!

Answer 30

No problem!