Answer :
To solve the problem of multiplying the expression [tex]\(x^9 \cdot x^5 \cdot x^4\)[/tex] using the product rule, follow these steps:
1. Identify the bases and exponents:
All the terms in the expression have the same base, which is [tex]\(x\)[/tex], with exponents 9, 5, and 4, respectively.
2. Use the product rule of exponents:
The product rule for exponents states that when you multiply terms with the same base, you add their exponents. In mathematical terms, this means:
[tex]\[
x^a \cdot x^b \cdot x^c = x^{a+b+c}
\][/tex]
3. Add the exponents:
For the expression [tex]\(x^9 \cdot x^5 \cdot x^4\)[/tex], you add the exponents:
[tex]\[
9 + 5 + 4 = 18
\][/tex]
4. Write the expression with the new exponent:
Applying the product rule, you get:
[tex]\[
x^{18}
\][/tex]
So, the expression [tex]\(x^9 \cdot x^5 \cdot x^4\)[/tex] simplifies to [tex]\(x^{18}\)[/tex].
1. Identify the bases and exponents:
All the terms in the expression have the same base, which is [tex]\(x\)[/tex], with exponents 9, 5, and 4, respectively.
2. Use the product rule of exponents:
The product rule for exponents states that when you multiply terms with the same base, you add their exponents. In mathematical terms, this means:
[tex]\[
x^a \cdot x^b \cdot x^c = x^{a+b+c}
\][/tex]
3. Add the exponents:
For the expression [tex]\(x^9 \cdot x^5 \cdot x^4\)[/tex], you add the exponents:
[tex]\[
9 + 5 + 4 = 18
\][/tex]
4. Write the expression with the new exponent:
Applying the product rule, you get:
[tex]\[
x^{18}
\][/tex]
So, the expression [tex]\(x^9 \cdot x^5 \cdot x^4\)[/tex] simplifies to [tex]\(x^{18}\)[/tex].
