Question
Express the following fraction in simplest form using only positive exponents. \[ \frac{12 u^{7}}{4(u)^{4}} \]
Ask by Franklin Boone. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of the fraction is \(3u^{3}\).
Solution
To simplify the fraction \(\frac{12 u^{7}}{4 u^{4}}\) using only positive exponents, follow these steps:
1. **Simplify the coefficients:**
\[
\frac{12}{4} = 3
\]
2. **Simplify the variables using the laws of exponents:**
\[
\frac{u^{7}}{u^{4}} = u^{7-4} = u^{3}
\]
3. **Combine the simplified coefficients and variables:**
\[
3u^{3}
\]
So, the fraction in its simplest form is:
\[
\boxed{3u^{3}}
\]
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Simplify this solution Bonus Knowledge
To simplify the fraction \(\frac{12 u^{7}}{4(u)^{4}}\), we start by simplifying the coefficients and then the variable part. 1. **Simplifying the coefficients:** \[ \frac{12}{4} = 3 \] 2. **Simplifying the variable part:** When dividing like bases, we subtract the exponents: \[ u^{7} \div u^{4} = u^{7-4} = u^{3} \] Combining these results gives us: \[ \frac{12 u^{7}}{4(u)^{4}} = 3 u^{3} \] Thus, the simplest form of the expression is: \[ \boxed{3u^{3}} \]
