College

Multiply the expression using the product rule:

[tex] x^9 \cdot x^5 \cdot x^4 [/tex]

[tex] x^9 \cdot x^5 \cdot x^4 = \square [/tex]

(Type exponential notation with positive exponents.)

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].