Question

1. $(-2k^2)^2$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((-2k^2)^2\), we can apply this rule where \(a = -2\), \(b = k^2\), and \(n = 2\). So we get \((-2)^2 \times (k^2)^2\).

Step2: Calculate each part

First, calculate \((-2)^2\). Squaring a negative number gives a positive result, so \((-2)^2 = 4\). Then, for \((k^2)^2\), we use the power of a power rule \((a^m)^n = a^{m \times n}\). Here, \(a = k\), \(m = 2\), and \(n = 2\), so \((k^2)^2 = k^{2 \times 2} = k^4\).

Step3: Multiply the results

Now, multiply the two results together: \(4 \times k^4 = 4k^4\).

Answer:

\(4k^4\)