Simplify a/a^3.
Understand the Problem
The question is asking for the simplification of a fraction that consists of an algebraic expression in the numerator and denominator. Specifically, we are simplifying the expression a/a^3.
Answer
The simplified expression is $$ \frac{1}{a^2} $$
Answer for screen readers
The simplified form of the expression is
$$ \frac{1}{a^2} $$
Steps to Solve
- Identifying the Expression The given expression is
$$ \frac{a}{a^3} $$
- Applying the Quotient Rule for Exponents When dividing like bases, we subtract the exponents. Here, the exponent of $a$ in the numerator is 1 and in the denominator is 3. So, we have:
$$ a^{1 - 3} $$
- Simplifying the Exponent Now simplify the exponent:
$$ a^{-2} $$
- Rewriting with Positive Exponent To express it with a positive exponent, we use the property of exponents:
$$ a^{-2} = \frac{1}{a^2} $$
The simplified form of the expression is
$$ \frac{1}{a^2} $$
More Information
The simplification of fractions is a common practice in algebra, helping to make expressions easier to work with. Understanding the rules of exponents is crucial for simplifying algebraic expressions efficiently.
Tips
- Forgetting to subtract exponents correctly.
- Not simplifying the expression fully, leaving it in the form of $a^{-2}$ instead of $\frac{1}{a^2}$.
- Confusing the rules for multiplying versus dividing exponents.
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