Question

simplify the following expression:
$(3y^4)^2$
options: $9y^8$, $6y^6$, $9y^6$, $6y^8$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For the expression \((3y^4)^2\), we apply this rule: \(3^2 \times (y^4)^2\).

Step2: Calculate each part

First, calculate \(3^2 = 9\). Then, use the power of a power rule \((a^m)^n = a^{m \times n}\) for \((y^4)^2\), so \(y^{4 \times 2}=y^8\).

Step3: Combine the results

Multiply the two results together: \(9 \times y^8 = 9y^8\).

Answer:

9y⁸ (corresponding to the first option)