College

Simplify the expression [tex](-7x^2)(x^4)[/tex].

A. [tex]-7x^6[/tex]
B. [tex]7x^6[/tex]
C. [tex]-7x^8[/tex]
D. [tex]-7x^3[/tex]

Answer :

To simplify the expression [tex]\((-7x^2)(x^4)\)[/tex], let's break it down step by step:

1. Identify the components in the expression: We have [tex]\(-7x^2\)[/tex] and [tex]\(x^4\)[/tex].

2. Multiply the coefficients: The coefficient in front of [tex]\(x^2\)[/tex] is -7, and the coefficient of [tex]\(x^4\)[/tex] is 1 (since it's just [tex]\(x^4\)[/tex]). When you multiply these coefficients together, you get [tex]\(-7 \times 1 = -7\)[/tex].

3. Multiply the powers of [tex]\(x\)[/tex]: According to the law of exponents, when you multiply same bases, you add the exponents. Here, we have [tex]\(x^2\)[/tex] and [tex]\(x^4\)[/tex]. So, you add the exponents: [tex]\(2 + 4 = 6\)[/tex].

4. Combine the results: The expression becomes [tex]\(-7x^{6}\)[/tex].

Therefore, the simplified expression is [tex]\(-7x^{6}\)[/tex].