Question

How do i simplify this math equation

Answer 1

`(1)/(9x^2)`

Explanation:

Hi! So to simplify this expression by using positive exponents, we are going to use an exponent rule.

One rule that we will be using is when we raise something to a negative power.

The rule is if we are raising something to negative power, like
`2^-3`, then we are going to write
`(1)/(2^3)`, which equals to 1/8

So, we bring 2^-3 to the bottom and make the exponent positive so instead of -3, it will be positive 3.

Another example: let's do
`4^(-2)`. We are going to write 1 over something. What is that something?

It is
`4^(2)`, or 16

So,
`4^(-2) =(1)/(4^2) =(1)/(16)`

In short, we write 1 over something and make the exponent positive

Example with variables:

Let's do
`(2x)^-2`:

We are going to write:
`(1)/((2x)^2)`

We brought whatever is raised to the power, which is 2x, to the bottom and made the exponent positive.

We can do some simplifying:
`(2x)^2` is the sames as (2x) multiplied by (2x). Multiply the 2's together and x's, and you get
`4x^2`

Now with our example: We are doing (-3x)^-2

We get:
`(1)/((-3x)&2)`

I brought the -3x to the bottom and made the exponent positive.

We can simplify the denominator by doing (-3x)^2, which is the same as -3x being multiplied by -3x.

-3 times -3 is 9, and x times x is x^2, so we get
`9x^2`

In short:
`(-3x)^2=(1)/((3x)^2) =(1)/(9x&2)`

Our final answer is:
`(1)/(9x^2)`

Hope this helps!