Examine the power.
${ }^4$
1. Identify the base: 5
2. Determine the exponent: 4
3. Write in expanded form: $5 \cdot 5 \cdot 5 \cdot 5$
What is the value of the power?
Answer (1)
We need to calculate the value of 5 4 .
This means multiplying 5 by itself 4 times: 5 × 5 × 5 × 5 .
Performing the multiplication step by step: 5 × 5 = 25 , 25 × 5 = 125 , and 125 × 5 = 625 .
The value of the power 5 4 is 625 .
Explanation
Understanding the Problem We are asked to find the value of the power 5 4 . This means we need to multiply 5 by itself 4 times.
Setting up the Calculation To calculate 5 4 , we perform the following multiplication:
5 × 5 × 5 × 5
First Multiplication First, we multiply 5 × 5 , which equals 25.
5 × 5 = 25
Second Multiplication Next, we multiply the result, 25, by 5:
25 × 5 = 125
Third Multiplication Finally, we multiply the new result, 125, by 5:
125 × 5 = 625
Final Answer Therefore, the value of 5 4 is 625.
625
Examples
Understanding powers is crucial in many areas, such as calculating compound interest. For example, if you invest $100 at an annual interest rate of 5%, compounded annually, the amount you'll have after 4 years is 100 × ( 1 + 0.05 ) 4 . Calculating ( 1.05 ) 4 involves raising 1.05 to the power of 4, similar to our problem. This concept extends to calculating areas and volumes, such as the area of a square ( s 2 ) or the volume of a cube ( s 3 ), where 's' is the side length.
