Sure, let's go through the multiplication of these terms step-by-step.
We need to multiply the two terms: [tex]\(2 a^{-1} \times 3 a^2\)[/tex].
1. Multiplying the coefficients:
- The first coefficient is [tex]\(2\)[/tex].
- The second coefficient is [tex]\(3\)[/tex].
- When multiplying coefficients together: [tex]\(2 \times 3 = 6\)[/tex].
2. Adding the exponents:
- The first exponent is [tex]\(-1\)[/tex].
- The second exponent is [tex]\(2\)[/tex].
- When multiplying terms with the same base, we add the exponents: [tex]\(-1 + 2 = 1\)[/tex].
Putting it all together, we have:
[tex]\[
2 a^{-1} \times 3 a^2 = 6 a^{1}
\][/tex]
or simply:
[tex]\[
6a
\][/tex]
So the final answer is [tex]\(6a\)[/tex].
