Question

simplify. express your answer as a single term, without a denominator.
( u^{5} cdot u^{4} )

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two terms with the same base, we add the exponents: \(a^m \cdot a^n = a^{m + n}\). Here, the base is \(u\), \(m = 8\), and \(n = 4\).

Step2: Apply the rule

So, \(u^8 \cdot u^4 = u^{8 + 4}\)

Step3: Calculate the sum of exponents

\(8 + 4 = 12\), so \(u^{8 + 4}=u^{12}\)

Answer:

\(u^{12}\)