# Question: Equation with Powers of 11

## Comment on Equation with Powers of 11

### At around 00:30 in the video,

At around 00:30 in the video, I didn't converted the 1/11^3 to 11^-3. Instead, I cross-multiplied like you would when solving a proportion; becoming: 11^8+4k=11^15. In the end, the answer was the same.

### Perfect! That works too.

Perfect! That works too.

### Do you have a few more

Do you have a few more problems like this that I can work through?

### Hi,

Hi,

There is something that seems very simple that I don't understand. I found -7/4 as a result because I did 12-8+4k = 4+4k. How do you find 4-4k?

Thanks,

### We want to simplify 12 - (8 +

We want to simplify 12 - (8 + 4k)
Here we're subtracting (8 + 4k) from 12, which means we must subtract 8 from 12 AND subtract 4k from 12.
So, 12 - (8 + 4k) = 12 - 8 - 4k = 4 - 4k

Here's another example;
Simplify 2x - (5 - 4x)
In this case, we're subtracting (5 - 4x) from 2x, which means we must subtract 5 from 2x AND subtract -4x from 2x
So, 2x - (5 - 4x) = 2x - 5 - (-4x) = 2x - 5 + 4x = 6x - 5

For more on this, check out my example at 4:42 in the following video: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

### I see the difference! Thank

I see the difference! Thank you, Again so close yet so far!

### plug in value here is a

plug in value here is a pretty good choice.

### Plugging in values will take

Plugging in values will take some time, but that strategy will definitely work!

### why -4k=-7 result in 4/7 but

why -4k=-7 result in 4/7 but not -4/-7?

### 4/7 and -4/-7 are equivalent

4/7 and -4/-7 are equivalent fractions.
Similarly, (-10) ÷ (-2) = 5 and 10 ÷ 2 = 5

Here, we're applying the rule that says (negative) ÷ (negative) = positive

### So it is implied that -7/-4

So it is implied that -7/-4 becomes positive even when it wasn't executed?

### Yes, the fraction -7/-4 is

Yes, the fraction -7/-4 is positive.
We can use equivalent fractions to show why: -7/-4 = (-1)(7)/(-1)(4) = (-1/-1)(7/4) = (1)(7/4) = 7/4