Question
Fully simplify using only positive exponents. \[ \frac{3 x^{6} y^{3}}{x^{2} y^{7}} \]
Ask by Watkins Cruz. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{3x^{4}}{y^{4}} \).
Solution
Calculate or simplify the expression \( \frac{3x^6y^3}{x^2y^7} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{3x^{6}y^{3}}{x^{2}y^{7}}\)
- step1: Simplify the expression:
\(\frac{3x^{6-2}y^{3}}{y^{7}}\)
- step2: Calculate:
\(\frac{3x^{4}y^{3}}{y^{7}}\)
- step3: Simplify the expression:
\(\frac{3x^{4}}{y^{7-3}}\)
- step4: Calculate:
\(\frac{3x^{4}}{y^{4}}\)
The fully simplified expression using only positive exponents is \( \frac{3x^{4}}{y^{4}} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify the expression \( \frac{3 x^{6} y^{3}}{x^{2} y^{7}} \), you can use the properties of exponents. First, divide the coefficients and then subtract the exponents of the same base. Starting with the coefficients: \[ \frac{3}{1} = 3 \] Next, for the \( x \) terms: \[ x^{6} \div x^{2} = x^{6-2} = x^{4} \] And for the \( y \) terms: \[ y^{3} \div y^{7} = y^{3-7} = y^{-4} \] Putting it all together: \[ 3 x^{4} y^{-4} \] Since we want only positive exponents, we can rewrite \( y^{-4} \) as \( \frac{1}{y^{4}} \): \[ 3 x^{4} \cdot \frac{1}{y^{4}} = \frac{3 x^{4}}{y^{4}} \] So the fully simplified expression is: \[ \frac{3 x^{4}}{y^{4}} \]
