Question

(m^4)^0 \cdot m^6

Explanation:

Step1: Apply the zero - exponent rule

The zero - exponent rule states that for any non - zero number \(a\), \(a^{0}=1\). In the expression \((m^{4})^{0}\), we can apply this rule. Since \(m\) (assuming \(m
eq0\)) is a non - zero base (in the context of exponent rules, if \(m = 0\), \(0^{0}\) is undefined, but we assume \(m
eq0\) here), so \((m^{4})^{0}=1\).

Step2: Multiply by \(m^{6}\)

Now we have the expression \((m^{4})^{0}\cdot m^{6}\), and we know from Step 1 that \((m^{4})^{0}=1\). So we multiply \(1\) by \(m^{6}\). When we multiply \(1\) by any number (or variable expression) \(x\), the result is \(x\). So \(1\cdot m^{6}=m^{6}\).

Answer:

\(m^{6}\) (corresponding to the option with \(m^{6}\))