Question

simplify.
\\((-2z^4x^2)^4\\)
write your answer without parentheses.

Explanation:

Step1: Apply the power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, for \((-2z^{4}x^{2})^{4}\), we can apply this rule to each factor inside the parentheses. That gives us \((-2)^4 \cdot (z^{4})^4 \cdot (x^{2})^4\).

Step2: Calculate each part

First, calculate \((-2)^4\). Since \((-2) \times (-2) \times (-2) \times (-2) = 16\). Then, for the exponents with variables, we use the power of a power rule \((a^m)^n = a^{m \times n}\). So, \((z^{4})^4 = z^{4 \times 4} = z^{16}\) and \((x^{2})^4 = x^{2 \times 4} = x^{8}\).

Step3: Multiply the results together

Now, multiply the results from Step 2: \(16 \cdot z^{16} \cdot x^{8} = 16z^{16}x^{8}\).

Answer:

\(16z^{16}x^{8}\)