How to use the POWER function
What is the POWER function?
The POWER function calculates a number raised to a power. You can also use the caret ^ character to perform a exponentiation in an Excel formula.
1. Introduction
What is exponentiation?
Exponentiation is a mathematical operation involving exponents. It means raising a number, known as the base, to a specified power. The exponent indicates how many times to multiply the base by itself.
baseexponent
Roots are the inverse operation, giving the base when the power and number are known. For example,
x5 = 3125
3125(1/5) = 5
x = 5
55 = 3125
This makes it possible to calculate roots using the POWER function, however, to calculate square roots you can also use the SQRT function.
How are roots and logarithms related?
Roots and logarithms are inverse mathematical operations:
A root "undoes" exponentiation, finding the base number when given the power and result.
For example, √16 = 4, since 42 = 16. The root reveals the base of 4. √16 = 16(1/2)
A logarithm is the inverse of exponentiation as well, returning the exponent that a base must be raised to in order to produce a number.
For example, =log(8,2) = 3, since 23 = 8. The logarithm returns the exponent 3.
Logarithms calculate the exponent and roots calculate the base. This example demonstrates how to calculate the exponent:
5x = 3125
LOG5(3125) = 5
x = 5
55 = 3125
What are the other logarithmic functions in Excel?
| Excel function | Description |
|---|---|
| LOG | Returns the logarithm with a given base. |
| LN | Returns the natural logarithm (base e) of a number |
| LOG10 | Returns the base-10 logarithm of a number |
The corresponding inverse functions for the logarithm functions in Excel:
| Logarithm | Power to |
|---|---|
| LOG | Arbitrary base, basex or POWER(number, power) |
| LN | EXP(number) |
| LOG10 | 10x or POWER(10,x) |
What are the exponentiation rules?
Product Rule: xm * xn = x(m+n)
Exponents with the same base are multiplied when multiplying terms.
Power Rule: (xm)n = x(m*n)
When raising a power to a power, the exponents are multiplied.
Power of a Product: (ab)n = an * bn
Exponents distribute to all factors in a product.
Quotient Rule: xm / xn = x(m-n)
Exponents with the same base subtract when dividing terms.
Power of Quotient: (a/b)n = an / bn
Exponents distribute to the numerator and denominator when raising a quotient.
Any base raised to the 0 power equals 1.
Negative Exponent Rule: x-n = 1 / xn
2. Syntax
POWER(number, power)
| number | Required. The number you want to raise. |
| power | Required. The exponent to which the number is raised. |
3. Example 1
The first example has the number in cell B3 and the power in cell C3. They are 5 and 2 respectively. The formula is in cell E3:
The result of 52 is 25, here is how:
52 = 5 * 5 = 25
The second example has the number 2 in cell B4 and the power 8 in cell C4. The formula is in cell E4:
The result of 28 is 256, here is how:
28 = 2 * 2 * 2* 2 * 2 * 2 * 2 * 2 = 256
The third example has the number in cell B5 and the power in cell C5. They are 10 and 2 respectively. The formula is in cell E5:
The result of 102 is 100, here is how:
102 = 10 * 10 = 100
The fourth example has the number 10 in cell B6 and the power 6 in cell C6. The formula is in cell E6:
The result of 106 is 256, here is how:
106 = 10 * 10 * 10 * 10 * 10 * 10 = 1,000,000
The fifth example has the number in cell B7 and the power in cell C7. They are 3 and 3 respectively. The formula is in cell E5:
The result of 33 is 27, here is how:
33 = 3 * 3 * 3 = 9 * 3 = 27
The sixth example has the number 4 in cell B6 and the power 3 in cell C6. The formula is in cell E6:
The result of 43 is 64, here is how:
43 = 4 * 4 * 4 = 64
4. Example 2
What is the area of a circle if the radius is 5 units?
The area of a circle is found by multiplying the mathematical constant pi (Ï€) by the square of the circle's radius.
A = π * r2
A = the area of the circle
r = the radius of the circle
Ï€ = pi
Formula in cell C23:
The area is approx. 78.54 square units based on a radius of 5 units. The PI function lets you calculate number pi, it has no arguments. The POWER function takes 5 to the power of 2 which is 25.
Lets plug the values and calculate the area manually. Here is how:
A = π * r2
A = 3.14159265358979 * 52
A = 3.14159265358979 * 25
A = 78.5398163397448
5. Example 3
A bacteria population doubles ever 1.5 hour. How many cells will you find after 7 hours if the start population is 50?
We need to find a pattern in the growth of the bacteria population over time and then use it to calculate the population after 7 hours.
Given information:
- The bacteria population doubles every 1.5 hours.
- The initial population is 50 cells.
The math formula has to be: Population = 50 * 2(t/1.5)
Formula in cell C21:
The formula returns 1269 cells after 7 hours with a start population of 50. The image above shows a chart illustrating an exponential blue cure, the x-axis title is hours and ranges from 0 to 7 hours. The y-axis title is population and ranges from 0 to 1400 cells.
Go to value 7 on the x-axis, follow an imaginary vertical line up until it intersects with the blue curve. The follow an imaginary horizontal line to the left until you find the y-axis. The y-axis value is near 1300 which corresponds to the calculated value in cell C21.
6. Example 4
If you invest $1,000 today in an account that pays 8% annual interest compounded annually, what will be the future value of your investment after 20 years?
We need to model a math function that follows the growth of the investment over time and then use it to calculate the amount after 20 years.
Given information:
- The investment compounds annually with an rate of 8%.
- The initial investment is 1,000.
The math formula has to be: Amount= 1000 * 1.08y
Formula in cell C21:
The formula returns 4,660 after 20 years with an initial investment of 1,000. The image above shows a chart illustrating an exponential blue cure, the x-axis represents years and ranges from 0 to 20 years. The y-axis title represents the amount and ranges from 1,000 to 5,000.
Go to year 20 on the x-axis, follow an imaginary vertical line up until it intersects with the blue curve. The follow an imaginary horizontal line to the left until you find the y-axis. The y-axis value is near 4600 which corresponds to the calculated amount in cell C21.
Comments
The ^ operator is easier to use, example 10^2 = 100, number^power.
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Functions in 'Math and trigonometry' category
The POWER function function is one of 61 functions in the 'Math and trigonometry' category.
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