Rewrite the product as an exponent: [tex]$p^3 p^{11}$[/tex]
Answer (2)
We have the expression p 3 p 11 .
Using the rule x a x b = x a + b , we add the exponents.
3 + 11 = 14 .
Therefore, the simplified expression is p 14 .
Explanation
Understanding the problem We are given the expression p 3 p 11 and we want to rewrite it as a single exponent. To do this, we need to remember the rule for multiplying exponents with the same base.
Applying the exponent rule The rule for multiplying exponents with the same base is: x a ⋅ x b = x a + b , where x is the base and a and b are the exponents. In our case, the base is p , and the exponents are 3 and 11.
Adding the exponents Now, we add the exponents: 3 + 11 = 14 .
Final result Therefore, we can rewrite the expression p 3 p 11 as p 14 .
Examples
Understanding how to simplify expressions with exponents is useful in many areas, such as calculating compound interest or understanding exponential growth in populations. For example, if a population of bacteria doubles every hour, the population after t hours can be represented as P 0 ". 2 t , where P 0 is the initial population. Simplifying such expressions helps in making predictions and understanding the behavior of the system.
The expression p 3 p 11 can be rewritten as a single exponent by adding the exponents. This results in p 14 . Therefore, the final simplified form is p 14 .
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