Question

question
simplify:
$(-7x^4)^2$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((-7x^4)^2\), we can apply this rule as \((-7)^2 \cdot (x^4)^2\).

Step2: Simplify each part

First, calculate \((-7)^2\). Squaring a negative number gives a positive result, so \((-7)^2 = 49\). Then, use the power of a power rule \((a^m)^n = a^{m \cdot n}\) for \((x^4)^2\). Here, \(m = 4\) and \(n = 2\), so \((x^4)^2 = x^{4 \cdot 2} = x^8\).

Step3: Combine the results

Multiply the two simplified parts together: \(49 \cdot x^8 = 49x^8\).

Answer:

\(49x^8\)