To simplify the given expression [tex]\(\left(-2 x^9\right)\left(8 x^2\right)\)[/tex], follow these steps:
1. Combine the coefficients (constant terms):
The coefficients in the expression are [tex]\(-2\)[/tex] and [tex]\(8\)[/tex]. By multiplying these coefficients, we get:
[tex]\[
-2 \times 8 = -16
\][/tex]
2. Combine the variable terms (exponents):
When multiplying terms with the same base, add the exponents. The variable terms are [tex]\(x^9\)[/tex] and [tex]\(x^2\)[/tex]. Therefore, we add the exponents:
[tex]\[
x^{9+2} = x^{11}
\][/tex]
3. Rewrite the expression with the simplified constants and exponents:
Combining the results from the previous steps, the expression simplifies to:
[tex]\[
-16x^{11}
\][/tex]
So, the simplified form of the expression [tex]\(\left(-2 x^9\right)\left(8 x^2\right)\)[/tex] is:
[tex]\[
-16x^{11}
\][/tex]
