- Identify the base as 5 and the exponent as 4.
- Expand the expression to \(5 \times 5 \times 5 \times 5\).
- Calculate the product sequentially: \(5 \times 5 = 25\), \(25 \times 5 = 125\), and \(125 \times 5 = 625\).
- Conclude that the value of \(5^4\) is \(\boxed{625}\).
Explanation
- Understanding the Problem
The problem asks us to evaluate the expression \(5^4\). An exponent of 4 means we need to multiply the base, which is 5, by itself 4 times. So, the expression is equivalent to \(5 \times 5 \times 5 \times 5\).
- Calculating the Value
To find the value, we perform the multiplication step by step:
- First, multiply the first two terms: \(5 \times 5 = 25\).
- Next, multiply the result by the third term: \(25 \times 5 = 125\).
- Finally, multiply this result by the fourth term: \(125 \times 5 = 625\).
Therefore, \(5^4 = 625\).
Examples
Calculating powers like \(5^4\) is essential in various fields, such as computer science when determining memory capacity or in finance when calculating compound interest. For example, if a population doubles every year, the growth over 4 years can be modeled by powers. Understanding exponentiation allows us to simplify repeated multiplication and handle large numbers efficiently in everyday real-world calculations.