Answer :
To simplify the expression [tex]\(9x^4 \cdot 4x^8\)[/tex], follow these steps:
1. Multiply the Coefficients: Start by multiplying the numerical coefficients (the numbers in front of the variables). In this case, it's 9 and 4.
[tex]\[
9 \times 4 = 36
\][/tex]
2. Add the Exponents of Like Bases: When you multiply terms that have the same base (in this case, the base is [tex]\(x\)[/tex]), you add the exponents.
- For [tex]\(x^4\)[/tex] and [tex]\(x^8\)[/tex], add the exponents:
[tex]\[
4 + 8 = 12
\][/tex]
3. Write the Simplified Expression: Combine the results of the above steps to write the simplified expression. You multiply the coefficients and write the base with the new exponent:
[tex]\[
36x^{12}
\][/tex]
Therefore, the simplified expression is [tex]\(36x^{12}\)[/tex].
1. Multiply the Coefficients: Start by multiplying the numerical coefficients (the numbers in front of the variables). In this case, it's 9 and 4.
[tex]\[
9 \times 4 = 36
\][/tex]
2. Add the Exponents of Like Bases: When you multiply terms that have the same base (in this case, the base is [tex]\(x\)[/tex]), you add the exponents.
- For [tex]\(x^4\)[/tex] and [tex]\(x^8\)[/tex], add the exponents:
[tex]\[
4 + 8 = 12
\][/tex]
3. Write the Simplified Expression: Combine the results of the above steps to write the simplified expression. You multiply the coefficients and write the base with the new exponent:
[tex]\[
36x^{12}
\][/tex]
Therefore, the simplified expression is [tex]\(36x^{12}\)[/tex].
