Question

simplify: $(3x^2)^3$
options: $27x^6$, $9x^5$, $9x^6$, $3x^6$

Explanation:

Step1: Apply power of a product rule

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

Step2: Calculate \(3^3\) and \((x^2)^3\)

First, calculate \(3^3\). We know that \(3^3 = 3\times3\times3 = 27\). Then, for \((x^2)^3\), we use the power of a power rule \((a^m)^n = a^{m\times n}\). So \((x^2)^3 = x^{2\times3}=x^6\).

Step3: Multiply the results

Multiply the results from Step 2: \(27\times x^6 = 27x^6\).

Answer:

A. \(27x^6\)