3ab^5 / 3a^8b
Understand the Problem
The question is asking for the simplification of the expression 3ab^5 / 3a^8b. The task is to reduce the expression to its simplest form by cancelling out like terms.
Answer
$$ \frac{b^4}{a^7} $$
Answer for screen readers
The simplest form of the expression is
$$ \frac{b^4}{a^7} $$
Steps to Solve
- Identify the expression The initial expression to simplify is given as:
$$ \frac{3ab^5}{3a^8b} $$
- Cancel common factors Notice that both the numerator and the denominator have a common factor of $3$. We can cancel it out:
$$ \frac{3ab^5}{3a^8b} = \frac{ab^5}{a^8b} $$
- Simplify the variables Now we simplify the variables. The variable $a$ is in both the numerator and denominator. We can apply the rule of exponents which states that $a^m / a^n = a^{m-n}$.
Thus, we simplify $a$:
$$ a^{1-8} = a^{-7} $$
- Simplify the remaining variable Now, we'll look at the $b$ terms. In the expression $b^5 / b$, we also apply the exponent rule:
$$ b^{5-1} = b^4 $$
- Combine the simplified terms Now we combine the simplified values:
$$ \frac{ab^5}{a^8b} = a^{-7}b^4 $$
- Rewrite in positive exponent form Lastly, to express with only positive exponents, we can rewrite $a^{-7}$ as $\frac{1}{a^7}$:
$$ a^{-7}b^4 = \frac{b^4}{a^7} $$
The simplest form of the expression is
$$ \frac{b^4}{a^7} $$
More Information
The process of simplifying fractions involves canceling out common factors in the numerator and denominator. This simplification is fundamental in algebra and helps to make calculations more manageable.
Tips
- Forgetting to cancel out the common factor of $3$ initially can lead to more complex results.
- Misapplying the exponent rules, such as forgetting that $a^m / a^n$ simplifies to $a^{m-n}$.
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