Question

4(x^3)^0, options: 4, 12, 0, 1

Explanation:

Step1: Recall the zero - exponent rule

The zero - exponent rule states that for any non - zero number \(a\), \(a^{0}=1\). Also, when we have \((a^{m})^{n}=a^{m\times n}\), but in the case of \((x^{3})^{0}\), using the power of a power rule \((x^{3})^{0}=x^{3\times0}=x^{0}\). And by the zero - exponent rule, since \(x\) (assuming \(x
eq0\)) is a non - zero number (if \(x = 0\), \(0^{0}\) is undefined, but in the context of this problem, we can assume \(x
eq0\) or the expression is defined), \(x^{0}=1\).

Step2: Simplify the expression \(4(x^{3})^{0}\)

Substitute \((x^{3})^{0}=1\) into the expression \(4(x^{3})^{0}\). We get \(4\times1 = 4\).

Answer:

4