108 to the Power of 8 = 108 ⁸ = 1.8509302102819E+16

Welcome to our exponent calculator! We're exploring the concept of "108 to the power of 8". Let's break down what this means and how to calculate it.

What are Exponents?

An exponent is a mathematical operation where we multiply a number (called the base) by itself a certain number of times (indicated by the power or exponent). In our case, 108 is the base, and 8 is the exponent.

Calculation

To calculate 108 to the power of 8, we multiply 108 by itself 8 times. Here's the step-by-step process:

Step	Calculation	Result
1	108	108
2	108 × 108	11664
3	108 × 108 × 108	1259712
4	108 × 108 × 108 × 108	136048896
5	108 × 108 × 108 × 108 × 108	14693280768
6	108 × 108 × 108 × 108 × 108 × 108	1586874322944
7	108 × 108 × 108 × 108 × 108 × 108 × 108	1.7138242687795E+14
8	108 × 108 × 108 × 108 × 108 × 108 × 108 × 108	1.8509302102819E+16

Solution: 108 to the power of 8 is equal to 1.8509302102819E+16.

How to write 108 to the power of 8 ?

Step 1: Understand the Concept

"108 to the power of 8" means we're multiplying 108 by itself 8 times. Let's break this down:

108 to the power of 8 = 108 × 108 × 108 × 108 × 108 × 108 × 108 × 108

Step 2: Learn the Notation

In mathematics, we have a special way to write this more concisely. We use superscript notation:

108⁸

Here, 108 is called the "base", and 8 is called the "exponent" or "power".

Step 3: Understand Alternative Notations

Sometimes, especially when typing or in programming, you might see it written as:

108⁸

This means the same thing as 108⁸.

Step 4: Calculate the Result

If we actually compute this:

108⁸ = 108 × 108 × 108 × 108 × 108 × 108 × 108 × 108 = 1.8509302102819E+16

Note: Remember, the exponent (8 in this case) tells us how many times to multiply the base (108) by itself.

Practice

Try writing these on your own:

107 to the power of 7
109 to the power of 9
8 to the power of 108

Interactive Power Calculator

Similar Calculations:

Number	Power	Answer
109	8	109⁸ = 1.9925626416902E+16
110	8	110⁸ = 2.14358881E+16
111	8	111⁸ = 2.3045377697176E+16
108	7	108⁷ = 1.7138242687795E+14

Related Mathematical Operations

Square Root

The square root is the inverse operation of squaring a number. For our example:

v1.7138242687795E+14 ≈ 13,091,311.1214

This is approximate because 108^8 isn't a perfect square.

Logarithm

Logarithms are the inverse of exponential functions. The logarithm of 1.7138242687795E+14 with base 108 should equal 8:

log₁₀₈(1.7138242687795E+14) = 8

Exponent Properties

1. Multiplying exponents with the same base: 108^a * 108^b = 108^(a+b)

Example: 108² * 108³ = 108⁵ = 14693280768

2. Dividing exponents with the same base: 108^a / 108^b = 108^(a-b)

Example: 108⁵ / 108² = 108³ = 1259712

108 to the Power of 8 = 108 8 = 1.8509302102819E+16