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Tutor-Verified Answer
Answer
The simplified form of the expression is \( \frac{abx^{3}}{c} \).
Solution
To simplify the expression:
\[
\frac{a x^{2} \cdot b x^{-3}}{c x^{-4}}
\]
**Step 1: Multiply the Numerator Terms**
First, multiply the terms in the numerator:
\[
a x^{2} \cdot b x^{-3} = ab \cdot x^{2 + (-3)} = ab \cdot x^{-1} = \frac{ab}{x}
\]
**Step 2: Divide by the Denominator**
Now, divide the result by the denominator:
\[
\frac{\frac{ab}{x}}{c x^{-4}} = \frac{ab}{x} \cdot \frac{1}{c x^{-4}} = \frac{ab}{c x} \cdot x^{4} = \frac{ab \cdot x^{4}}{c x}
\]
**Step 3: Simplify the Expression**
Combine the \( x \) terms:
\[
\frac{ab \cdot x^{4}}{c x} = \frac{ab}{c} \cdot x^{4 - 1} = \frac{ab}{c} \cdot x^{3} = \frac{abx^{3}}{c}
\]
**Final Simplified Form:**
\[
\frac{abx^{3}}{c}
\]
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Simplify this solution The Deep Dive
To simplify the expression \( \frac{a x^{2} b x^{-3}}{c x^{-4}} \), first, combine the terms in the numerator: \( ax^{2}b x^{-3} = ab x^{2 - 3} = ab x^{-1} \). Now, rewrite the entire expression: \[ \frac{ab x^{-1}}{c x^{-4}} = \frac{ab}{c} \cdot x^{-1 - (-4)} = \frac{ab}{c} \cdot x^{3} \] So, the simplified expression is \( \frac{ab}{c} x^{3} \). Engaging with simplifying expressions is much like finding a secret path in a maze; you're in for a fun adventure as you uncover the beauty of mathematical structure! When dealing with variables, always remember: combine powers and keep track of those pesky negative exponents. It’s all about tidying up your math life!
