Final answer:
To solve this expression without using exponents, we can apply the basic principles of multiplication. When multiplying two expressions with the same base, we add the exponents. In this case, both expressions have a base of p. Therefore, we can add the exponents 3 and 2 to get a final exponent of 5. This gives us the final answer of p⁵.
Step-by-step explanation:
To understand how to write p³ x p² without exponents, we must first understand the concept of exponents and how they work. Exponents are a shorthand notation used to represent repeated multiplication. For example, p³ can be written as p x p x p. Similarly, p² can be written as p x p. Therefore, p³ x p² can be written as (p x p x p) x (p x p).
To solve this expression without using exponents, we can apply the basic principles of multiplication. When multiplying two expressions with the same base, we add the exponents. In this case, both expressions have a base of p. Therefore, we can add the exponents 3 and 2 to get a final exponent of 5. This gives us the final answer of p⁵.
Explanation continued:
Now, let's break down the process of solving p³ x p² without exponents in more detail. First, we can rewrite p³ as p x p x p and p² as p x p. Next, we can use the commutative property of multiplication to rearrange the terms and group them together based on their common base. This gives us (p x p) x (p x p x p).
Next, we can use the associative property of multiplication to rearrange the terms within the parentheses. This gives us (p x p) x (p x p) x p. Since p x p is equal to p², we can substitute this into our expression to get (p²) x (p²) x p.
Using the basic principles of multiplication, we can then multiply the coefficients first, which gives us 1 x 1 x 1 = 1. This leaves us with the final expression of (p²)⁵, which can be simplified to p⁵.
In summary, to write p³ x p² without exponents, we first rewrite the expressions using repeated multiplication. Then, we use the properties of multiplication to rearrange and group the terms based on their common base. Finally, we use the basic principles of multiplication to simplify the expression and arrive at our final answer of p⁵.