# How do you simplify #(-10)^5/ (-10)^9#?

##### 3 Answers

#### Explanation:

#### Explanation:

When, in a fraction, the same quantity appears as a multiplicative factor in both numerator and denominator, it can be simplified.

By multiplicative factor, I mean that you can simplify the

but not here:

In your case, the factors stand alone, so they can be simplified. Just remember the very definition of power as reiterated multiplication to write (I'm setting

As you can see, the same quantity

So, the answer is

**N.B.:** in general, when you have the same quantity appearing in both numerator and denominator, you can simply perform some exponent algebra to get

the reason is exactly the reiterated multiplication cancelation that I just showed you. In this example, in fact, you had

Negative exponent means to consider the inverse of the positive exponent, and in fact we have

#### Explanation:

Question: Simplify

Using the index rule that

Our expression is now

The next parts don't necessarily simplify the answer, but they make it a bit easier to visualise.

A negative power means we put one over our answer; think of it as a special case of the index rule above, but where n = 0.

Our expression is now

We know that a number to an even power can be even or odd (like