## Exponent Calculator

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 *bases* *with* both *negative* *exponents* and *positive* *exponents*. It also provides a step by step method with an accurate answer.

## What is an exponent?

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 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 *exponent* *calculator* 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 = 3^{4}

**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 of* *exponent* for *2 raise to power* 9 (2 to the 9th power)

It means = 2^{9}

**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 = 5^{4}, 6^{4}, 7^{4}

**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.*

0.1 to the power of 3 | 0.00100 |

0.5 to the power of 3 | 0.12500 |

0.5 to the power of 4 | 0.06250 |

1.2 to the power of 4 | 2.07360 |

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 |

1.4 to the 10th power | 28.92547 |

1.05 to the power of 5 | 1.27628 |

1.05 to the 10th power | 1.62889 |

1.06 to the 10th power | 1.79085 |

2 to the 3rd power | 8 |

2 to the power of 3 | 8 |

2 raised to the power of 4 | 16 |

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 | 268435456 |

3 to the power of 2 | 9 |

3 to the 3 power | 27 |

3 to the 4 power | 81 |

3 to the 8th power | 6561 |

3 to the 9th power | 19683 |

3 to the 12th power | 531441 |

3 to what power equals 81 | 3^{4} |

4 to the power of 3 | 64 |

4 to the power of 4 | 256 |

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 |

12 to the power of 3 | 1728 |

10 exponent 3 | 1000 |

24 to the second power (24^{2}) | 576 |

10 to the power of 3 | 1000 |

3 to the power of 5 | 243 |

6 to the power of 3 | 216 |

9 to the power of 3 | 729 |

9 to the power of 2 | 81 |

10 to the power of 5 | 100000 |

**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 5^{0}.

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,

5^{0}= 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 1/3^{-2}.

We will first make the power positive by taking reciprocal.

1/3^{-2}=3^{2}

3^{2} = 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 (2^{6})(2^{2}).

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

(2^{6})(2^{2}) = 2^{6+2}

2^{8} =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 3^{7 }/3^{2}

3^{7}/ 3^{2}=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: ( x^{2})^{3}.

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

(x^{2})^{3}=x^{2*3}

= x^{6}

**Power of a product property:**

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

**Example: **Simplify (4*5)^{2}

**4**^{2}*******5**^{2}**=16*****25**

= 400

**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}=2^{2 }/ 3^{2}

2^{2}/ 3^{2}=4/9

**References:**

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