Simplify the Algebraic Expression: Calculating x^3 × x^2 × x^{-2} × x^4

To solve this problem, we'll apply the rules for multiplying exponents:

• Step 1: Identify the exponents on the base $x$: - $x^3$ has an exponent of 3. - $x^2$ has an exponent of 2. - $x^{-2}$ has an exponent of -2. - $x^4$ has an exponent of 4.
• Step 2: Apply the multiplication rule for exponents, which states that when multiplying like bases you add the exponents:
• Calculate the total exponent by summing all individual exponents: $x^{3+2+(-2)+4}$.
• Step 3: Simplify the sum of the exponents:

$3 + 2 - 2 + 4 = 7$

Thus, the expression simplifies to $x^7$.

Therefore, the simplified result of the given expression is $x^7$.

Upon evaluating the given choices, the correct answer choice is option 4: $x^7$.