To simplify the expression [tex]\( x^4 \cdot x^3 \cdot x \)[/tex], we can follow these steps:
1. Understand the multiplication of powers property: When multiplying expressions that have the same base, we add the exponents. This property is written as:
[tex]\[
a^m \cdot a^n = a^{m+n}
\][/tex]
2. Identify the base and exponents: In the given expression [tex]\( x^4 \cdot x^3 \cdot x \)[/tex], the base is [tex]\( x \)[/tex], and the exponents are 4, 3, and 1 respectively. (Note that [tex]\( x \)[/tex] without an exponent explicitly written has an implied exponent of 1.)
3. Sum the exponents: Add the exponents together:
[tex]\[
4 + 3 + 1 = 8
\][/tex]
4. Write the simplified expression: Combine the base [tex]\( x \)[/tex] with the total exponent from the addition:
[tex]\[
x^8
\][/tex]
Therefore, the simplified form of the expression [tex]\( x^4 \cdot x^3 \cdot x \)[/tex] is:
[tex]\[
x^8
\][/tex]
