Which expression is equivalent to 3a^3b^4c / 6a^5b for all positive values of a, b and c?
Understand the Problem
The question is asking which expression is equivalent to the given algebraic expression for positive values of a, b, and c. The goal is to simplify or manipulate the expression to find an equivalent form.
Answer
The equivalent expression is $$ \frac{bc}{2a^2} $$.
Answer for screen readers
The expression equivalent to
$$ \frac{3a^3b^4c}{6a^5b} $$
is
$$ \frac{bc}{2a^2} $$.
Steps to Solve
- Identify the expression We start with the expression:
$$ \frac{3a^3b^4c}{6a^5b} $$
- Simplify the coefficients First, simplify the numerical coefficients:
$$ \frac{3}{6} = \frac{1}{2} $$
So we have:
$$ \frac{1a^3b^4c}{2a^5b} $$
- Simplify the variable (a) Next, we simplify the (a) terms using the property (a^m / a^n = a^{m-n}):
$$ \frac{a^3}{a^5} = a^{3-5} = a^{-2} $$
This gives us:
$$ \frac{1b^4c}{2a^2b} $$
- Simplify the variable (b) Now simplify the (b) terms in the same way:
$$ \frac{b^4}{b^1} = b^{4-1} = b^{3} $$
Thus, we have:
$$ \frac{bc}{2a^2} $$
- Final expression The simplified expression is:
$$ \frac{bc}{2a^2} $$
The expression equivalent to
$$ \frac{3a^3b^4c}{6a^5b} $$
is
$$ \frac{bc}{2a^2} $$.
More Information
This simplification reduces the complexity of the expression by breaking down the coefficients and variables into simpler parts, following the rules of exponents and arithmetic operations.
Tips
- Forgetting to simplify the coefficients: It's easy to overlook the numerical part before simplifying variables.
- Misapplying the exponent rules, like not subtracting correctly when simplifying.
To avoid these mistakes, double-check each step and ensure you're applying the rules correctly.
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