Question

selected response: 1 point for correct answer
simplify: $(5m^{4})^{2}$
$25m^{8}$
$10m^{8}$
$5m^{8}$
$5m^{6}$

Explanation:

Step1: Apply power of a product rule

To simplify \((5m^4)^2\), we use the power of a product rule \((ab)^n = a^n b^n\). Here, \(a = 5\), \(b = m^4\), and \(n = 2\). So we can rewrite it as \(5^2\times(m^4)^2\).

Step2: Calculate the powers

First, calculate \(5^2\), which is \(25\). Then, for \((m^4)^2\), we use the power of a power rule \((a^m)^n=a^{m\times n}\), so \((m^4)^2 = m^{4\times2}=m^8\).

Step3: Multiply the results

Multiply the two results together: \(25\times m^8 = 25m^8\).

Answer:

A. \(25m^8\)