Math Calculators ▶ Exponent Calculator
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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!
Read on!
You can also use our online scientific notation calculator that allows you to add, subtract, multiply or divide any numbers in scientific notation.
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.
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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.
There are some basic rules for the exponentiation with their examples. Lets have a look at rules & examples :
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:
\((3^2)(3^4) = 3^{2+4} \)
\((3^2)(3^4) = 3^6\)
\((3^2)(3^4) = 3*3*3*3*3*3\)
\((3^2)(3^4) = 729\)
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:
\( {\frac{5^6}{5^4}} = 5^{6-4}\)
\( {\frac{5^6}{5^4}} = 5^2\)
\( {\frac{5^6}{5^4}} = 25\)
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.
\(7^0 = 1\)
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:
\((y^3)^4 = y^{3*4}\)
\((y^3)^4 = y^{12}\)
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:
\((4*3)^3 = 4^3*3^3\)
\((4*3)^3 = 64*27\)
\((4*3)^3 = 1728\)
When the two integers are dividing and having the same power, then both integers have the same power separately. Eg;
\({(\frac{m}{n})^x} = {\frac{m^x}{n^x}}\)
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.
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.
Just follow the given steps for the accurate results.
Swipe on!
Inputs:
Outputs:
Now, the exponent finder shows:
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:
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From the source of Wikipedia: Definition & rules of exponentiation
From the site of Sciencing.com : How to find it manually.
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