Question

simplify. express your answer using positive exponents.
$u^{-40} \cdot u \cdot u^{-6}$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying terms with the same base, we add the exponents: \(a^m \cdot a^n = a^{m + n}\). Here, the base is \(u\), and we have \(u^{-40} \cdot u \cdot u^{-6}\). Note that \(u = u^1\).

Step2: Add the exponents

So we add the exponents: \(-40 + 1 + (-6)\). First, \(-40+1=-39\), then \(-39 + (-6)=-45\). So the expression becomes \(u^{-45}\).

Step3: Convert to positive exponent

Recall that \(a^{-n}=\frac{1}{a^n}\), so \(u^{-45}=\frac{1}{u^{45}}\).

Answer:

\(\frac{1}{u^{45}}\)