Question

number 11
$(2x^2)^3$

Explanation:

Step1: Apply power of a product rule

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

Step2: Simplify each term

First, calculate \(2^3 = 8\). Then, use the power of a power rule \((a^m)^n = a^{m \times n}\) for \((x^2)^3\), so \(x^{2 \times 3}=x^6\).

Step3: Multiply the results

Multiply the two simplified terms: \(8 \times x^6 = 8x^6\).

Answer:

\(8x^6\)