Exponent Calculator

The exponentiation of a base is a mathematical operation, written as an, where a is the base and n is the exponent. Exponentiation of a positive integer corresponds to repeated multiplication by n.

aⁿ = a × a × ... × a

        n times

Negative bases can be entered into the above calculator, but imaginary numbers cannot be computed. In addition, it does not accept fractions, but it can be used to compute fractional exponents if the exponents are input in decimal form. The exponent calculator is used for calculating values for exponential expressions. Normally, such an expression is composed of two elements - the base and the power (exponent). Both negative and positive exponents may be used. Input the values into the input box to use the exponent calculator.

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Fraction Exponent Calculator  

If an exponent of a numeral is a fraction, it is denoted as a fractional exponent. Exponents display the number of times a numeral is repeated in multiplication. For illustration, 5² = 5×5 = 25. The numeral says x^1/y, x is the base, and 1/y is the fractional exponent.

Fraction exponent calculator puts calculation of both exponents and radicals into exponential form.

• To calculate exponents such as 2 raised to the power of 2 you would enter 2 raised to the fraction power of \[(\frac {2}{1})\] or 2^2/1.

• To calculate radicals such as the square root of 25, you would enter 25 raised to the power of \[(\frac {1}{2})\].

• To calculate combined exponents and radicals such as the 4th root of 16 raised to the power of 5 you would enter 16 raised to the power of \[(\frac {5}{4})\] or 16^5/4 where x = 16, n = 5 and d = 4.

• If you try to take the root of a negative number, your answer may be NaN = Not a Number.

Exponent calculator variables can also be used with various types of fractions.

Let us take an example, 7^5/2

Here,

7 represents the base

\[(\frac {5}{2})\] represents the fraction exponent, 5 is the numerator and 2 is the denominator.

Calculate Fraction Exponents Using the Fraction Exponent Calculator?

Here is the fraction exponential calculator with steps:

Step 1: Enter the base and exponent into the appropriate input fields

Step 2: Click on "Solve" to get a result

Step 3: Last but not least, the fractional exponent calculator variables are displayed in the output section.

How Does an Exponent Calculator Work?

Exponents are used to representing how many times a number is multiplied by itself. Assume that we have a base denoted by x and that its corresponding power is given by n. The expression is written as an. This implies that the base x has been multiplied n times by itself.

It is very useful to represent very large or very small numbers with exponents. When we have a negative exponent, it means that the reciprocal of the base is being multiplied repeatedly. X-n is reciprocal. This means that 1/x is being multiplied n times. We can also multiply fractions by exponents. These types of exponents represent powers and roots together. Let's assume that an exponent is represented as x^1/2. This notation indicates that we must take the square root of the number x. We can also represent cube roots in the same way. Decimal exponents are also a type of exponent. This type of exponent is expressed in decimals. To evaluate such exponents, we must convert the decimal to a fraction.

Laws of Exponents

1. Multiplication of powers with the same base.

2. Powers can be divided based on the same base.

3. The power of a power.

4. Multiplying power with the same exponent.

5. Negative exponents.

6. Exponentiation of power.

7. The exponent is in fractional form.

Exponents Rules

Solved Examples on Exponents:

Example 1: Find the exponential value for 10³ and verify it using the exponent calculator algebra.

Solution:

Base = 10

Exponent = 3

10³ = 10 × 10 × 10  = 1000

Example 2: Find the exponential value for 36^0.5 and verify it using the exponent calculator algebra.

Solution:

Base = 36

Exponent = 0.5. This can also be denoted as \[\frac {1}{2}\],

Thus, we have to find the square root of 49.

36^0.5 = 36^1/2 = 6. 

How to Use Exponent Keys?

Imagine what you want is to be the value. In most exponent calculators, you enter the base, then press the exponent key, followed by the exponent.  

For example:

Enter 10, then press the exponent key, then enter 5. This means the calculator should display 100,000 because that's the same as 105. But before you start making a list of calculations, you should do a simple test to make sure your calculator doesn't require you to input the exponent first. 

Press the exponent key to enter the number 2, followed by the number 3. You should see the number 8. You see 9 since the calculator interpreted 23 as 32 rather than 23 as input. This means you need to enter the exponent before the base.

There is a key marked YX on some calculators. It corresponds to the ^ key. Hit the Enter or = key, then enter 10, then yx, and then 5 to find 105.

Conclusion:

With this free online multiplying exponent calculator, calculating exponents for both negative and positive integers has become very easy. You can add, subtract, multiply and divide large numbers just as you would small ones, and the results will continue to appear in scientific notation as long as they continue to have too many digits to display. Both students and professionals can make good use of this tool, just stick with it to solve your related-problems with the multiplying exponent calculator.