Question

exponents and exponential functions
introduction to the product rule of exponents
simplify.
$u^4 \cdot u^3$

Explanation:

Step1: Recall the product rule of exponents

The product rule of exponents states that for any real number \( a \) and positive integers \( m \) and \( n \), \( a^m \cdot a^n = a^{m + n} \). Here, the base \( a \) is \( u \), \( m = 4 \), and \( n = 3 \).

Step2: Apply the product rule

Using the product rule, we add the exponents of the same base. So, \( u^4 \cdot u^3 = u^{4 + 3} \).

Step3: Simplify the exponent

Calculate \( 4 + 3 = 7 \). Thus, \( u^4 \cdot u^3 = u^7 \).

Answer:

\( u^7 \)