# Exponent Question

1. Jul 4, 2008

### benr2424

Hello everyone!

The following question stumped me and I thought you may be able to help.

If x^y = 2 and x^t = 16 what does x^(y-t) equal?

I don't know where to start so any help would be appreciated.
Thanks,
Ben

Last edited: Jul 4, 2008
2. Jul 4, 2008

### jostpuur

You should be clearer with the notation. By x^y-t, do you mean (x^y)-t or x^(y-t)? The notation looks like (x^y)-t, but I'm probably not wrong when guessing that you meant x^(y-t)?

3. Jul 4, 2008

### rock.freak667

Assuming you meant that you wanted to find $x^{y-t}$, if $a^n \times a^m = a^{n+m}$, can you split $x^{y-t}$ into the product of two exponents?

4. Jul 4, 2008

### benr2424

Sorry, the notation in the problem was given as such:

....what does x^(y-t) equal?

5. Jul 4, 2008

### rock.freak667

Do you know the rules regarding indices?

6. Jul 4, 2008

### Kaimyn

When you say x$$^{y-t}$$ it's the same as $$\frac{x^{y}}{x^{t}}$$
First we need to find x, y and t.
So if x$$^{y}$$ = 2, and x$$^{t}$$ = 16, then x needs to be even. It also needs to be able to divide those numbers into whole integers. Now the only number that fits into those catagories is 2.
2, however, could be positive or negative. But the fact that x$$^{1}$$ is 2, means that it cannot be a negative number.

So we know x=2, y=1 and t=4 (2*2*2*2 = 16). If that is the case, then x$$^{y-t}$$ = 2$$^{1-4}$$ = 2$$^{-3}$$ = $$\frac{1}{2*2*2}$$ = $$\frac{1}{8}$$ = 0.125

OR: $$\frac{x^{y}}{x^{t}}$$ = $$\frac{2^{1}}{2^{4}}$$ = $$\frac{2}{16}$$ = $$\frac{1}{8}$$ = 0.125

7. Jul 5, 2008

### Werg22

?!

We do not know to know either x, t or y. x^y-t = x^y / x^t = 2 / 16 = 1/8. Voila.

8. Jul 5, 2008

### Kaimyn

Good point... Ahh well, either gives you the right answer. However, you could use it as reference for checking.

9. Jul 6, 2008

### benr2424

Thanks everyone!! 1/8 is the correct answer!