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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

See 8 prime factorization.

The prime factorization of 12

2 * 2 * 3 =
22 * 3

See 12 prime factorization.

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-43

The problem is solved.