Does anyone know how to simplify x^5 * x^-3?

Question

Does anyone know how to simplify x^5 * x^-3?

Answer 1

(x^5)(x^(-3)) = x^5 / x^3 = x^2.

Answer 2

Since both bases are the same (x), all you have to do is add the exponents. For things like this, it's helpful to think of a simpler example.

If we have 2^2 * 2^-1 we can progress as follows:

2^2 * 2^-1=
4 * 1/2=
2=
2^1

All we've done is added the exponents of the original:

2^(2+ -1) = 2^1 = 1

For your problem, we have

x^5 * x^-3 = x^(5+ -3) = x^2

Answer 3

Add the indices when multiplying.

1. y^5 * y^3 = y^8 , derived from (5+3)

2. y^-5 * y^3 = y^-2 , derived from (-5+3)

3. y^5 * y-3 = y ^2 , derived form [5 + (-3)]

4. y^-5 * y^-3 = y^-8 , derived form [-5 + (-3)]

In you are dividing, subtract the second index form the first index.

Answer 4

Since x is the base, you just have to add the 2 exponents together and you get x^2

Answer 5

Yes.

x^(5 - 3) = x^2 = xx.

Answer 6

regroup this using the following idea. a^z*a*y=a^(z+y)

so for your problme x^5*x^-3=x^(5-3)=x^2

Answer 7

x^2

When you multiply terms with exponents, you add the exponents.

x^5 * x^-3 =
x^2