Question

use the problem shown to write a general rule for simplifying the expression $x^2 \cdot x^5$.$x^2 \cdot x^5LXB0= x^7$a. $x^{2(5)}$b. $x^{2 - 5}$c. $x^{2 + 5}$d. $x^{2/5}$

Explanation:

Step1: Analyze the given example

We have $x^2 \cdot x^5$, which expands to $x(x) \cdot x(x)(x)(x)(x)$. Counting the $x$ terms: $2 + 5 = 7$, so it equals $x^7$.

Step2: Match to general rule

The operation that takes $2$ and $5$ to $7$ is addition, so the general rule is $x^a \cdot x^b = x^{a+b}$. For $a=2, b=5$, this is $x^{2+5}$.

Answer:

C. $x^{2+5}$