# SBP-Program

## Rules of simplifying fractions with negative exponents

What are the rules for simplifying fractions with negative exponents?

### Simple rules for simplifying fractions with negative exponents

Rules for simplifying fractions with negative exponents:

1. Factor the numerator and denominator of the fraction;
2. Find common factors to both the numerator and denominator;
3. Cancel down all the common factors.

### Examples of simplifying fractions with negative exponents

Problem 1: Simplify the fraction with negative exponents

8a-6
12a-4

Solution.

Step by step.

1. Factor the numerator and denominator of the fraction.

The prime factorization of 8

2 * 2 * 2 =
23

The prime factorization of 12

2 * 2 * 3 =
22 * 3

2. Find common factors to both the numerator and denominator.

We have

8a-6 = 12a-4
22 * a-4 * 2 * a-2
22 * a-4 * 3

The common factors are 22 and a-4.

3. Cancel down all the common factors.

Cancel the common factors

(22 * a-4) * 2 * a-2 = (22 * a-4) * 3
(22 * a-4) * 2 * a-2 = (22 * a-4) * 3
2a-2
3

4. The answer is

8a-6 2a-2 = 12a-4 3

The problem is solved.