Question

simplify. express your answer as a single term, without a denominator. ( u^0 cdot u^4 )

Explanation:

Step1: Recall exponent rule \(a^m \cdot a^n = a^{m + n}\) and \(a^0 = 1\) (for \(a

eq0\))
First, simplify \(u^0\). By the zero - exponent rule, any non - zero number (or variable) raised to the power of 0 is 1. So \(u^0=1\) (assuming \(u
eq0\)).

Step2: Apply the product of powers rule

Now we have \(u^0\cdot u^4\). Substitute \(u^0 = 1\) into the expression, we get \(1\cdot u^4\). But we can also use the product of powers rule directly. The product of powers rule states that for the same base \(a\), \(a^m\cdot a^n=a^{m + n}\). Here, the base \(a = u\), \(m = 0\) and \(n = 4\). So \(u^0\cdot u^4=u^{0 + 4}\).

Step3: Simplify the exponent

Simplify the exponent \(0+4 = 4\). So \(u^{0 + 4}=u^4\).

Answer:

\(u^4\)