Sure! Let's simplify the expression [tex]\(\left(-3 x^{-2}\right)\left(4 x^4\right)\)[/tex] step-by-step.
1. Distribute the constants:
[tex]\[
\left(-3 x^{-2}\right) \left(4 x^4\right)
\][/tex]
First, we can multiply the constants [tex]\(-3\)[/tex] and [tex]\(4\)[/tex]:
[tex]\[
-3 \cdot 4 = -12
\][/tex]
2. Combine the exponents of [tex]\(x\)[/tex]:
According to the property of exponents, [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex], we can combine the terms with the variable [tex]\(x\)[/tex]:
[tex]\[
x^{-2} \cdot x^4 = x^{(-2 + 4)}
\][/tex]
3. Add the exponents:
[tex]\[
-2 + 4 = 2
\][/tex]
So we have:
[tex]\[
x^{2}
\][/tex]
4. Combine the results:
Now, multiply the constants and the variable part:
[tex]\[
-12 \cdot x^2
\][/tex]
Therefore, the simplified form of the expression [tex]\(\left(-3 x^{-2}\right)\left(4 x^4\right)\)[/tex] is:
[tex]\[
-12x^2
\][/tex]
