Simplify the expression: $x^n \cdot x^3$
Answer (1)
Identify the expression to simplify: x n × x 3 .
Apply the exponent property: x a × x b = x a + b .
Add the exponents: n + 3 .
The simplified expression is x n + 3 .
Explanation
Understanding the problem We are given the expression x n × x 3 to simplify.
Simplifying the expression We need to use the properties of exponents to simplify this expression.
Using exponent properties The property of exponents states that when multiplying two powers with the same base, we add the exponents: x a × x b = x a + b .
Applying the property Applying this property to the given expression, we have x n × x 3 = x n + 3 .
Final Answer Therefore, the simplified expression is x n + 3 .
Examples
Understanding how to simplify expressions with exponents is crucial in many areas, such as calculating growth rates or dealing with polynomial expressions. For example, if you're analyzing the growth of a bacteria colony where the growth rate is exponential, you might encounter expressions like 2 t × 2 3 , where t is time. Simplifying this to 2 t + 3 helps you easily understand how the colony size changes over time. This skill is also fundamental in more advanced topics like calculus and differential equations.
