Question
Simplify the expression: \( \left(\frac{-4 r^{5} s^{3}}{r}\right)^{3} \) \( 64 r^{12} s^{9} \) \( -64 r^{4} s^{6} \) \( -4 r^{12} s^{9} \) \( -64 r^{12} s^{9} \)
Ask by Ellis Powell. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \( -64 r^{12} s^{9} \).
Solution
To simplify the expression \( \left(\frac{-4 r^{5} s^{3}}{r}\right)^{3} \), follow these steps:
1. **Simplify Inside the Parentheses:**
\[
\frac{-4 r^{5} s^{3}}{r} = -4 r^{5-1} s^{3} = -4 r^{4} s^{3}
\]
2. **Raise to the Power of 3:**
\[
(-4 r^{4} s^{3})^{3} = (-4)^{3} \cdot (r^{4})^{3} \cdot (s^{3})^{3} = -64 r^{12} s^{9}
\]
**Final Simplified Expression:**
\[
-64 r^{12} s^{9}
\]
**Among the provided options, the correct simplified form is:**
\[
-64 r^{12} s^{9}
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
To simplify the expression \( \left(\frac{-4 r^{5} s^{3}}{r}\right)^{3} \), we first simplify the fraction inside the parentheses: \[ \frac{-4 r^{5} s^{3}}{r} = -4 r^{4} s^{3} \] Now we raise this expression to the power of 3: \[ \left(-4 r^{4} s^{3}\right)^{3} = (-4)^{3} (r^{4})^{3} (s^{3})^{3} \] Calculating each part, we find: \[ (-4)^{3} = -64, \quad (r^{4})^{3} = r^{12}, \quad (s^{3})^{3} = s^{9} \] Putting it all together: \[ -64 r^{12} s^{9} \] So, the simplified expression is: \(-64 r^{12} s^{9}\) It's the correct option from the choices given!
