To simplify the expression [tex]\(7 y^2 \cdot -3 y^5\)[/tex], we need to follow a series of steps that involve handling both the numerical coefficients and the exponents separately. Here's a step-by-step solution:
1. Identify and Combine the Coefficients:
The coefficients here are [tex]\(7\)[/tex] and [tex]\(-3\)[/tex].
- When multiplying these coefficients together, we get:
[tex]\[
7 \cdot (-3) = -21
\][/tex]
2. Handle the Exponents:
The exponents involve the same base, [tex]\(y\)[/tex].
- When we multiply expressions with the same base, we add the exponents. So for [tex]\(y^2\)[/tex] and [tex]\(y^5\)[/tex], we have:
[tex]\[
y^2 \cdot y^5 = y^{2+5} = y^7
\][/tex]
3. Combine the Results:
Now, putting it all together, we multiply the combined coefficient with the combined exponents:
[tex]\[
7 y^2 \cdot -3 y^5 = -21 y^7
\][/tex]
Thus, the simplified form of the given expression [tex]\(7 y^2 \cdot -3 y^5\)[/tex] is:
[tex]\[
-21 y^7
\][/tex]
Therefore, the correct answer is:
a. [tex]\(-21 y^7\)[/tex]
