48 to the Power of 6 = 48 ⁶ = 12230590464

Welcome to our exponent calculator! We're exploring the concept of "48 to the power of 6". 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, 48 is the base, and 6 is the exponent.

Calculation

To calculate 48 to the power of 6, we multiply 48 by itself 6 times. Here's the step-by-step process:

Step	Calculation	Result
1	48	48
2	48 × 48	2304
3	48 × 48 × 48	110592
4	48 × 48 × 48 × 48	5308416
5	48 × 48 × 48 × 48 × 48	254803968
6	48 × 48 × 48 × 48 × 48 × 48	12230590464

Solution: 48 to the power of 6 is equal to 12230590464.

How to write 48 to the power of 6 ?

Step 1: Understand the Concept

"48 to the power of 6" means we're multiplying 48 by itself 6 times. Let's break this down:

48 to the power of 6 = 48 × 48 × 48 × 48 × 48 × 48

Step 2: Learn the Notation

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

48⁶

Here, 48 is called the "base", and 6 is called the "exponent" or "power".

Step 3: Understand Alternative Notations

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

48⁶

This means the same thing as 48⁶.

Step 4: Calculate the Result

If we actually compute this:

48⁶ = 48 × 48 × 48 × 48 × 48 × 48 = 12230590464

Note: Remember, the exponent (6 in this case) tells us how many times to multiply the base (48) by itself.

Practice

Try writing these on your own:

47 to the power of 5
49 to the power of 7
6 to the power of 48

Interactive Power Calculator

Similar Calculations:

Number	Power	Answer
49	6	49⁶ = 13841287201
50	6	50⁶ = 15625000000
51	6	51⁶ = 17596287801
48	5	48⁵ = 254803968

Related Mathematical Operations

Square Root

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

v254803968 ≈ 15,962.5802

This is approximate because 48^6 isn't a perfect square.

Logarithm

Logarithms are the inverse of exponential functions. The logarithm of 254803968 with base 48 should equal 6:

log₄₈(254803968) = 6

Exponent Properties

1. Multiplying exponents with the same base: 48^a * 48^b = 48^(a+b)

Example: 48² * 48³ = 48⁵ = 254803968

2. Dividing exponents with the same base: 48^a / 48^b = 48^(a-b)

Example: 48⁵ / 48² = 48³ = 110592

48 to the Power of 6 = 48 6 = 12230590464