To simplify the expression [tex]\( 7.5 y^4 \cdot 9 y^2 \)[/tex], we will follow these steps:
1. Multiply the coefficients: The coefficients are the numerical parts of the terms. In this case, we have [tex]\(7.5\)[/tex] and [tex]\(9\)[/tex].
[tex]\[ 7.5 \times 9 \][/tex]
This multiplication results in:
[tex]\[ 67.5 \][/tex]
2. Add the exponents of [tex]\(y\)[/tex]: The variable [tex]\(y\)[/tex] has exponents [tex]\(4\)[/tex] and [tex]\(2\)[/tex] in the given expression. According to the laws of exponents, when you multiply two terms with the same base, you add their exponents. Thus, we add the exponents [tex]\(4\)[/tex] and [tex]\(2\)[/tex]:
[tex]\[ 4 + 2 \][/tex]
This results in:
[tex]\[ 6 \][/tex]
Putting these together, the complete simplified expression is:
[tex]\[ 67.5 y^6 \][/tex]
Thus, the correct answer is:
a. [tex]\(67.5 y^6\)[/tex]
