Question

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

Explanation:

Step1: Analyze the given example

We have $x^2 \cdot x^5 = \underbrace{x \cdot x}_{2\text{ times}} \cdot \underbrace{x \cdot x \cdot x \cdot x \cdot x}_{5\text{ times}} = x^{2+5} = x^7$

Step2: Identify the general rule

When multiplying two exponential terms with the same base, we add the exponents. For $x^a \cdot x^b$, the result is $x^{a+b}$. In this case, $a=2$ and $b=5$, so the rule is $x^{2+5}$.

Answer:

D. $x^{2+5}$