Simplify each expression.
$(4x^3{y}^2{z}^3{)}^2$

• A. $8x^6{y}^4{z}^6$
• B. $16x^6{y}^4{z}^6$
• C. $16x^3{y}^2{z}^3$
• D. $4x^3{y}^4{z}^6$

Answer: (B)

Verified step by step guidance

1. Recall the Power of a Product Rule, which states that for any numbers \(a\) and \(b\), and any exponent \(n\), \((ab)^n = a^n b^n\). This means you raise each factor inside the parentheses to the power outside.
2. Identify the base factors inside the parentheses and the exponent outside. For example, if you have \((xy)^3\), the base factors are \(x\) and \(y\), and the exponent is \(3\).
3. Apply the Power of a Product Rule by raising each factor inside the parentheses to the exponent separately. Using the example, \((xy)^3 = x^3 y^3\).
4. If the problem includes coefficients or more complex expressions inside the parentheses, apply the exponent to each part accordingly. For example, \((2ab)^4 = 2^4 a^4 b^4\).
5. Simplify each term if possible by calculating powers of numbers or variables, but do not combine unlike bases. This completes the application of the Power of a Product Rule.