3x^3/9x^3 simplify

Question

The question is about properties of exponents and i tried and i got 3x^-5. Is that right, and can you have a number to the negative power?

Answer 1

 (3x³) / (9x³)

(3/9)(x³ / x³)

(1/3)(1)

1/3

 

a^x / a^y = a^x-y

Answer 2

If the question is (3x³/9x³) -- which I think it is -- you would have to simplify by using the rules of exponents. 

 

First, let us think about what the problem really says. The top of the fraction is 3x³. Another way to say that is 3xxx.

The bottom of the fraction is 9x³. Another way to say that is 9xxx. 

 

So, the fraction looks like this:

 

3xxx

9xxx

 

By the fact that anything divided by itself is 1, we can cancel out all of the x's in the expression. 

 

3xxx
9xxx

 

so, we are left with just 3/9. If you reduce this, this becomes 1/3. 

 

To answer your other question - yes, you can have a number to a negative power. A negative power can be put into a fraction. 

 

I hope this helps!

 

Frank