What is 4 to the 5th power?

To find 4 to the 5th power, we are essentially multiplying the number 4 by itself a total of five times. This is a fundamental concept in mathematics known as exponentiation, where the base (in this case, 4) is raised to an exponent (in this case, 5). Let's break it down step by step.

Calculating 4 to the 5th Power

The expression can be written as:

4^5

This means:

4 × 4 × 4 × 4 × 4

Step-by-Step Multiplication

Now, let's perform the multiplication step by step:

• First, multiply the first two 4s:

4 × 4 = 16

• Next, take that result and multiply it by the next 4:

16 × 4 = 64

• Now, multiply that result by the next 4:

64 × 4 = 256

• Finally, multiply by the last 4:

256 × 4 = 1024

The Final Result

After performing all these multiplications, we find that:

4^5 = 1024

Understanding Exponents

Exponentiation is a powerful tool in mathematics. It allows us to express large numbers in a compact form. For example, instead of writing out all the multiplications, we can simply write 4^5. This concept is widely used in various fields, including science, engineering, and finance, where dealing with large quantities is common.

Real-World Applications

Understanding powers and exponents can help in many practical situations. For instance, in computer science, algorithms often involve exponential growth, and in finance, compound interest calculations can be expressed using exponents. Knowing how to manipulate these numbers can provide significant advantages in problem-solving.

In summary, 4 to the 5th power equals 1024, and grasping how to calculate and apply exponents is a valuable skill in both academic and real-world contexts.