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Simplify. \( \frac{16 y^{2} z}{4 y^{5} z^{2}} \)

Ask by Maxwell Whittaker. in the United States
Feb 26,2025

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The simplified expression is \( \frac{4}{y^{3} z} \).

Solución

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)

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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 \(\frac{4}{y^{3} z}\).

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