To simplify the expression [tex]\(\left(\frac{5}{4} x^6 y^2\right)\left(3 x^3 y\right)\)[/tex], we can follow these steps:
1. Separate and multiply the coefficients:
- Take the coefficient from the first term, which is [tex]\(\frac{5}{4}\)[/tex].
- Take the coefficient from the second term, which is [tex]\(3\)[/tex].
- Multiply these coefficients together:
[tex]\[
\frac{5}{4} \times 3 = \frac{5 \times 3}{4} = \frac{15}{4} = 3.75
\][/tex]
2. Combine the exponents for the variable [tex]\(x\)[/tex]:
- The exponent of [tex]\(x\)[/tex] in the first term is [tex]\(6\)[/tex].
- The exponent of [tex]\(x\)[/tex] in the second term is [tex]\(3\)[/tex].
- When multiplying terms with the same base, add the exponents:
[tex]\[
x^6 \times x^3 = x^{6+3} = x^9
\][/tex]
3. Combine the exponents for the variable [tex]\(y\)[/tex]:
- The exponent of [tex]\(y\)[/tex] in the first term is [tex]\(2\)[/tex].
- The exponent of [tex]\(y\)[/tex] in the second term is [tex]\(1\)[/tex].
- When multiplying terms with the same base, add the exponents:
[tex]\[
y^2 \times y = y^{2+1} = y^3
\][/tex]
4. Form the simplified expression:
- Combine the simplified coefficient with the simplified variable expressions:
[tex]\[
3.75 \cdot x^9 \cdot y^3
\][/tex]
Thus, the simplified expression is:
[tex]\[
\left(\frac{5}{4} x^6 y^2\right)\left(3 x^3 y\right) = 3.75 \cdot x^9 \cdot y^3
\][/tex]
