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Exponents Calculator or e calculator is used in solving exponential forms of expressions. It is also known as raised to the power calculator.

Properties of exponents calculator:

This calculator solves baseswith both negativeexponents and positiveexponents. It also provides a step by step method with an accurate answer.

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What is an exponent?

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An exponent is a small number located in the upper, right-hand position of an exponential expression (base exponent), which indicates the power to which the base of the expression is raised.

The exponent of a number shows you how many times the number is to be used in a multiplication. Exponents do not have to be numbers or constants; they can be variables.

They are often positive whole numbers, but they can be negative numbers, fractional numbers, irrational numbers, or complex numbers. It is written as a small number to the right and above the base number.

Types:

There are basically two types of exponents.

• Positive exponent

A positive exponent tells how many times a number is needed to be multiplied by itself. Use our exponentcalculator to solve your questions.

• Negative exponent

A negative exponent represents which fraction of the base, the solution is. To simplify exponents with power in the form of fractions, use our exponent calculator.

Example:

Calculate the exponent for the 3 raised to the power of 4 (3 to the power of 4).

It means = 3⁴

Solution:

3*3*3*3 = 81

4 to the 3rd power = 81

Therefore the exponent is 81

2 raised to the power calculator.

Example:

What is the value ofexponent for 2 raise to power 9 (2 to the 9th power)

It means = 2⁹

Solution:

2*2*2*2*2*2*2*2*2 = 512

2 to the 9th power = 512

Therefore the exponent is 512.

Example:

How do you calculate the exponents of 5,6,7 to the power of 4?

It means = 5⁴, 6⁴, 7⁴

Solution:

5*5*5*5 = 625

6*6*6*6 = 1296

7*7*7*7 = 2401

Therefore the exponents are 625, 1296, 2401.

How to calculate the nth power of a number?

The nth power of a base, let’s say “y”, means y multiplied to itself nth time. If we are to find the fifth power of y, it is y*y*y*y*y.

Some other solutions for the nth power calculator are in the following table.

Exponent Rules:

Learning the exponent rules along with log rules can make maths really easy for understanding. There are 7 exponent rules.

• Zero Property of exponent:

It means if the power of a base is zero then the value of the solution will be 1.

Example: Simplify 5⁰.

In this question, the power of base is zero, then according to the zero property of exponents, the answer of this non zero base is 1. Hence,

5⁰= 1

• Negative Property of exponent:

It means when the power of base is a negative number, then after multiplying we will have to find the reciprocal of the answer.

Example: Simplify 13^-2.

We will first make the power positive by taking reciprocal.

1/3^-2=3²

3² = 9

• Product Property of exponent:

When two exponential expressions having the same non zero base and different powers are multiplied, then their powers are added over the same base.

Example: Solve (2⁶)(2²).

As it is obvious, bases are the same so powers are to be added. Now

(2⁶)(2²) = 2⁶+2

2⁸ =2*2*2*2*2*2*2*2

=256

• Quotient Property of exponent:

It is the opposite of the product property of exponent. When two same bases having different exponents are required to be divided, then their powers are subtracted.

Example: Simplify 3⁷ /3²

3⁷ / 3²=3^7-2

35=3*3*3*3*3

= 243

• Power of a Power Property:

When an exponent expression further has power, then firstly you need to multiply the powers and then solve the expression.

Example: Solve: ( x²)³.

Keeping in view the power of power property of exponents, we will multiply powers.

(x²)³=x^2*3

= x⁶

• Power of a product property:

When a product of bases is raised to some power, the bases will possess the power separately.

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Example: Simplify (4*5)²

4² * 5²=16*25

= 400

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• Power of a Quotient Property:

It is the same as the power of a product property. Power belongs separately to both the numerator and denominator.

Example: Solve (2/3)²

(2/3)²=2² / 3²

2² / 3²=4/9

References:

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1. Mclph.umn.edu. 2020. What Is An Exponent?.
2. Stapel, E., 2020. Exponents: Basic Rules Purplemath.
3. Math.com. 2020. Algebra Basics - Exponents - In Depth.
4. Mathinsight.org. 2020. Basic Rules For Exponentiation - Math Insight.
5. Analyzemath.com. 2020. What Are Exponents In Maths - Grade 7 Maths Questions With Detailed Solutions.