Question
Simplify. \( \frac{16 y^{2} z}{4 y^{5} z^{2}} \)
Ask by Maxwell Whittaker. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{4}{y^{3} z} \).
Solution
We start with the expression:
(16 y² z) / (4 y⁵ z²)
Step 1: Simplify the numerical coefficients.
16 ÷ 4 = 4
Step 2: Simplify the y terms using the rule yᵃ/yᵇ = y^(a - b):
y² ÷ y⁵ = y^(2 − 5) = y^(−3)
Step 3: Simplify the z terms similarly:
z ÷ z² = z^(1 − 2) = z^(−1)
Putting it all together:
4 · y^(−3) · z^(−1) = 4 / (y³ z)
Thus, the simplified expression is:
4 / (y³ z)
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To simplify the expression \( \frac{16 y^{2} z}{4 y^{5} z^{2}} \), we can break it down step by step. First, simplify the coefficients: \( \frac{16}{4} = 4 \). Next, simplify the \( y \) terms: \( \frac{y^{2}}{y^{5}} = \frac{1}{y^{5-2}} = \frac{1}{y^{3}} \). Now, simplify the \( z \) terms: \( \frac{z}{z^{2}} = \frac{1}{z^{2-1}} = \frac{1}{z} \). Now, putting it all together, we get: \[ \frac{16 y^{2} z}{4 y^{5} z^{2}} = 4 \cdot \frac{1}{y^{3}} \cdot \frac{1}{z} = \frac{4}{y^{3} z}. \] So, the simplified form of the expression is \(\frac{4}{y^{3} z}\).
