more properties of exponents

Question

(x^-2x^-3)⁴

 

 

Answer 1

When we have exponents inside and outside like this, what we need to do it multiply the exponent values together:

-2 * 4 = -8

-3 * 4 = -12

So that means we have x^-8x^-12 so far.

 

Essentially x^-2 * x^-2 * x^-2 * x^-2 as an example of what's happening here, and if you remember from previous lessons, if you have this set-up, you would add/subtract the exponents together:

-2 - 2 - 2 - 2 = -8 once again.

Similarly, -3 - 3 - 3 - 3 = -12, and that still gives us our answer of  x^-8x^-12.

 

Now, since our variable's the same, we can again add/subtract our exponents together:

-8 - 12 = -20

That means our final answer is going to be x^-20

Answer 2

If you have the same bases you can add the exponents.

 

So x^-2x^-3 = x^-5  = (1/x⁵)⁴ = (1⁴)/(x⁵)⁴ = (1/x²⁰) or x^-20