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The negative exponent rule is a key concept in algebra. It states that any number or variable raised to a negative exponent can be rewritten as a fraction. Specifically, if you have an expression like \( x^{-a} \), it equals \( \frac{1}{x^a} \).
This helps simplify expressions because it changes a negatively exponentiated term into a more manageable positive exponent.
Let’s see an example to grasp this concept better:
Suppose you have the term \( (m^4)^{-1} \). According to the rule, this becomes \( \frac{1}{m^4} \).
Remember to apply this rule whenever you encounter negative exponents in your expressions.

A double fraction occurs when you have a fraction inside another fraction. Simplifying these can seem tricky, but the process is straightforward: convert the double fraction into a simpler multiplication problem.
For instance, an expression like \( \frac{\frac{1}{m^4}}{9m^3} \) can be made more manageable by transforming it into a division: \( \frac{1}{m^4} \) divided by \( 9m^3 \).
Remember that dividing by a fraction is the same as multiplying by its reciprocal. So, \( \frac{1}{m^4} \) divided by \( 9m^3 \) is the same as multiplying \( \frac{1}{m^4} \) by \( \frac{1}{9m^3} \).
After this step, you're left with a more familiar operation involving the multiplication of fractions.

Once you've reduced a double fraction to a multiplication problem, you need to multiply the fractions. Here's how you do it: multiply the numerators together and the denominators together.
For example, with \( \frac{1}{m^4} \times \frac{1}{9m^3} \), you multiply the numerators \( 1 \times 1 = 1 \) and the denominators \( m^4 \times 9m^3 = 9m^{7} \) (since \( m^4 \times m^3 = m^{4+3} \)).
Thus, the product of the fractions is \( \frac{1}{9m^7} \).
This is your simplified expression. Practice these steps, and you'll master the art of simplifying complex fractions efficiently!