Question

simplify. express your answer using a single exponent. \\((x^{11})^0\\)

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 power of a power, \((a^{m})^{n}=a^{m\times n}\), but in the case where the exponent is \(0\), we can directly apply the zero - exponent rule. For the expression \((x^{11})^{0}\), regardless of the value of the base (as long as the base is defined, and for \(x^{11}\), \(x\) can be any real number, and when we raise it to the power of \(0\)), we use the rule that \(a^{0} = 1\) (here \(a=x^{11}\)).

Step2: Apply the zero - exponent rule

Using the zero - exponent rule \(a^{0}=1\) where \(a = x^{11}\), we get \((x^{11})^{0}=1\).

Answer:

\(1\)