# How do you simplify #(5x ^ { 3} ) ( 2x ) ^ { - 3}#?

##### 2 Answers

#### Explanation:

When you see some term raised to a negative power, it's really shorthand for division.

In other words,

So

Notice that the

At this point, we notice that

And **so this is our final answer**.

*Note: It is also appropriate to mention that #x ne 0#, since if #x = 0# then #(5x^3) / (8x^3) = 0 / 0# and one cannot divide by zero.*

#### Explanation:

First, let's rewrite this without the negative exponent. The negative means that the term is in the denominator:

Now, let's distribute the power in the denominator:

The last step is to cancel out the

We can do this because any number divided by itself is 1 which means:

We can also approach the original problem a different way.

After we distribute the

Now when we simplify this equation we get:

After rearranging this expression we can then use the rules of exponents. When you multiply terms with the same base you add their exponents together: