Answer :
To simplify the product [tex]\(5x^9 \cdot 4x^7\)[/tex], follow these steps:
1. Multiply the coefficients (numbers in front of the variables):
- The coefficients here are 5 and 4.
- Multiply these together: [tex]\(5 \times 4 = 20\)[/tex].
2. Add the exponents of the like bases:
- Both terms have the base [tex]\(x\)[/tex].
- For exponentiation with the same base, you add the exponents: [tex]\(x^9 \cdot x^7\)[/tex].
- Add the exponents: [tex]\(9 + 7 = 16\)[/tex].
3. Write the simplified expression:
- Combine the multiplied coefficient with the base [tex]\(x\)[/tex] raised to the sum of the exponents.
- This gives you: [tex]\(20x^{16}\)[/tex].
So, the product in its simplest form is [tex]\(20x^{16}\)[/tex].
1. Multiply the coefficients (numbers in front of the variables):
- The coefficients here are 5 and 4.
- Multiply these together: [tex]\(5 \times 4 = 20\)[/tex].
2. Add the exponents of the like bases:
- Both terms have the base [tex]\(x\)[/tex].
- For exponentiation with the same base, you add the exponents: [tex]\(x^9 \cdot x^7\)[/tex].
- Add the exponents: [tex]\(9 + 7 = 16\)[/tex].
3. Write the simplified expression:
- Combine the multiplied coefficient with the base [tex]\(x\)[/tex] raised to the sum of the exponents.
- This gives you: [tex]\(20x^{16}\)[/tex].
So, the product in its simplest form is [tex]\(20x^{16}\)[/tex].
