To find the product of the two terms \((7x^2 y^3)(3x^5 y^8)\), we will follow the rules of multiplying coefficients and adding the exponents of like terms.
1. Multiply the coefficients:
- The coefficients are \(7\) and \(3\).
- Multiplying these gives \(7 \times 3 = 21\).
2. Add the exponents of the \(x\) terms:
- The first term has \(x^2\) and the second term has \(x^5\).
- Adding the exponents: \(2 + 5 = 7\).
3. Add the exponents of the \(y\) terms:
- The first term has \(y^3\) and the second term has \(y^8\).
- Adding the exponents: \(3 + 8 = 11\).
Combining these results, the product of the terms is:
[tex]\[ 21 x^7 y^{11} \][/tex]
Comparing this to the given options:
- \(10 x^7 y^{11}\)
- \(10 x^{10} y^{24}\)
- \(21 x^7 y^{11}\)
- \(21 x^{10} y^{24}\)
The correct answer is:
[tex]\[ 21 x^7 y^{11} \][/tex]
