What is 3 to the power of 4?
"3 to the power of 4" is a mathematical expression that represents the repeated multiplication of the number 3 by itself, four times. It is often written as 3⁴ and pronounced "three to the fourth power" or "three raised to the power of four."
How to calculate 3 to the power of 4:
To calculate 3⁴, we need to multiply 3 by itself four times:
3⁴ = 3 x 3 x 3 x 3
Let's break it down step by step:
- 3 x 3 = 9
- 9 x 3 = 27
- 27 x 3 = 81
Therefore, 3⁴ = 81.
Understanding the concept:
The power (or exponent) in a mathematical expression indicates how many times the base number is multiplied by itself. In this case, the base is 3 and the exponent is 4.
Example:
Let's say you have a cube with each side measuring 3 units. The volume of this cube can be calculated using the formula:
Volume = side x side x side
Since each side is 3 units, the volume is:
Volume = 3 x 3 x 3 = 27 cubic units
This is the same as saying the volume is 3³ (3 to the power of 3).
More examples:
- 2⁵ = 2 x 2 x 2 x 2 x 2 = 32 (2 to the power of 5)
- 5² = 5 x 5 = 25 (5 to the power of 2)
Conclusion:
In conclusion, 3 to the power of 4 represents the repeated multiplication of 3 by itself four times, resulting in 81. Understanding the concept of exponents is crucial in mathematics and its applications in various fields like physics, engineering, and computer science.