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# Exponent Calculator

Base (b)

Exponent (x)

Table of Content
 1 What is an Exponent? 2 Basic Rules: 3 How to Calculate Exponents for Any Integer (Step-by-Step):
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An online exponent calculator helps you to solve the exponent operations and determine the value of any positive or negative integer raised to nth power. Also, this exponential calculator shows the results of the fractional or negative power of any number. Here we provide you all the related data of exponent, manual calculations, exponentiation rules and much more. Let’s have a look at some basics!

You can also use our online scientific notation calculator that allows you to add, subtract, multiply or divide any numbers in scientific notation.

## What is an Exponent?

In Mathematics, it indicates how many copies of a number multiply together. For example; $$7^4$$ , 7 is base and 4 is the exponent. In this example 4 copies of 7 are multiplied together to give 2401 as 7*7*7*7.

It is very easy to do the calculations with small values but for large & decimal bases or for the negative or fractions, large powers, use our fraction exponent calculator.

### Basic Rules:

There are some basic rules for the exponentiation with their examples. Lets have a look at rules & examples :

#### Product rule:

When multiplying a base term by two different exponents, then the resultant of both the powers is the power of base. E;g

$$a^m.a^n = a^{m+n}$$

Example:

Solve $$(3^2)(3^4)$$?

Solution:

This is equals to the:

$$(3^2)(3^4) = 3^{2+4}$$

$$(3^2)(3^4) = 3^6$$

$$(3^2)(3^4) = 3*3*3*3*3*3$$

$$(3^2)(3^4) = 729$$

#### Quotient Rule:

When dividing a base term by two different exponents, then the difference of both the powers is the power of base. E;g

$${\frac{a^m}{a^n}} = a^{m-n}$$

Example:

Determine the answer of the following exponentiation operation $${\frac{5^6}{5^4}}$$ ?

Solution:

By applying the quotient rule:

$${\frac{5^6}{5^4}} = 5^{6-4}$$

$${\frac{5^6}{5^4}} = 5^2$$

$${\frac{5^6}{5^4}} = 25$$

#### Zero Rule:

The exponent of any number will be equal to 1. E;g

$$b^0 = 1$$

Where b is any integer (positive or negative)

Example:

Solve $$7^0$$?

Solution:

In tis equation the power of the base 7 is zero, so according to this rule the answer of this non zero base is 1.

$$7^0 = 1$$

#### Power of exponent:

When an integer having the power of its exponent, then both the powers are multiplied together to get the single power. Eg;

$$({a^m})^{n} = {a}^{mn}$$

Example:

Solve $$(y^3)^4$$?

Solution:

Both powers get multiplied together to give the single power to the base:

$$(y^3)^4 = y^{3*4}$$

$$(y^3)^4 = y^{12}$$

#### Power of the product of two numbers:

When the product of two integers having the power, then both the integers have the same power separately. Let’s have a look:

$$(ab)^x = a^x*b^x$$

Example:

Simplify $$(4*3)^3$$?

Solution:

According to the rule:

$$(4*3)^3 = 4^3*3^3$$

$$(4*3)^3 = 64*27$$

$$(4*3)^3 = 1728$$

#### Power of the quotient of two numbers:

When the two integers are dividing and having the same power, then both integers have the same power separately. Eg;

$${(\frac{m}{n})^x} = {\frac{m^x}{n^x}}$$

#### Negative power property:

When the power of the some integer is the negative number, then it will be equal to the reciprocal of the number.

$$a^-x = {\frac{1}{a^x}}$$

This best and free negative exponent calculator considers these exponent properties and calculate power of any integer accurately. Also, you can try our online log and antilog calculator which is the inverse of the exponent function.

## How to Calculate Exponents for Any Integer (Step-by-Step):

The calculations for power become easy with this power calculator, which helps to do the calculations for all the integers (negative, positive, fractions). Ahead to manual example:

Example:

Find 3 to the power 7?

Solution:

The formula is:

$$(x)^n = x*x*x*x*……..n$$

Here, x is 3 & n is 7. So,

$$(3)^7= 3*3*3*3*3*3*3$$

$$(3)^7= 2187$$

Further, if you have negative or fractional bases or exponents, then give a try to our online negative exponent calculator that helps you to determine the speedy results of negative or fractional inputs.

## How to Use Online Exponents Calculator:

Just follow the given steps for the accurate results.

Swipe on!

Inputs:

• First of all, enter the base value.
• Then, enter the power to which how many times a base multiply with itself.
• Lastly, click on calculate button.

Outputs:

Now, the exponent finder shows:

• The value of your input data.
• Step-by-Step calculations.

## End-Note:

Now, calculating exponents for both negative as well as positive integers become very easy with this free online exponent calculator. This tool works best for both students & professionals, just stick with it to solve your related-problems.

Here we provide you the table of some common values of integers with their powers:

 0.1 to the power of 3 0.001 0.1 to the power of 4 0.0001 0.2 to the power of 3 0.008 0.5 to the power of 3 0.125 0.5 to the power of 4 0.0625 0.5 to the power of 3 0.125 1.2 to the power of 4 2.0736 1.02 to the 10th power 1.21899 1.03 to the 10th power 1.34392 1.2 to the power of 5 2.48832 1.3 to the power of 5 3.71293 1.3 to the power of 3 2.197 1.4 to the 10th power 28.9255 1.05 to the power of 5 1.27628 1.05 to the power of 3 1.15762 1.05 to the 10th power 1.62889 1.06 to the 10th power 1.79085 2 to the power of 3 8 2 raised to the power of 4 16 2 to the power of 5 32 2 to the power of 6 64 2 to the power of 7 128 2 to the 9th power 512 2 to the tenth power 1024 2 to the 15th power 32768 2 to the 10th power 1024 2 to the power of 28 2.68435e+08 3 to the power of 2 9 3 to the 3 power 27 3 to the 4 power 81 3 to the power of 5 243 3 to the 8th power 6561 3 to the 9th power 19683 3 to the 12th power 531441 3 to what power equals 81 34 4 to the power of 3 64 4 to the power of 4 256 4.3 to the power of 5 1470.08 4 to the power of 7 16384 7 to the power of 3 343 12 to the 2nd power 144 2.5 to the power of 3 15.625 2.19 to the power of 5 50.3756 12 to the power of 3 1728 10 exponent 3 1000 24 to the second power (242) 576

## References:

From the source of Wikipedia: Definition & rules of exponentiation

From the site of Sciencing.com : How to find it manually.