Power of a Number – Definition, Rules, Explanation, Examples | How to Calculate Powers and Exponents

In this article, students will completely understand the concept of the Power of a Number. We all know how to calculate the product of the number but if we have to find the product of the same number for n times then we can represent it as powers or exponents.

Learn the definitions of power, exponent, and many more along with basic rules for powers of the number. Also, you will find the solved examples on number powers or exponents calculations from this page so practice well and get a good grip on the topic.

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Powers and Exponents – Definition

We have an idea to find the value for the expression 2 x 2 x 2. But this expression can be defined in a shorter way with the help of powers and exponents.

ie., 2 x 2 x 2= 2³

An expression that denotes repeated multiplication of the same factor is known as a power.

The number 2 is called the base, and the number 3 is known as the exponent.

powers and exponents

How to Find the Power of a Number without a Calculator?

The power of a number is also known as Exponents. Calculation exponents are very simple. Just follow the steps on how to solve exponents for both positive and negative numbers from here and practice some solved examples too for a better understanding of the concept.

Steps for Positive Exponents

Find the base and power it is raised to.
Write the base of the same number of times as exponent.
Place a multiplication symbol between each base and multiply the same.

Steps to Find Exponent for Negative Numbers

Define the base and power it is raised to.
Address the reciprocal of the base and turn the sign of the exponent to positive.
Write the reciprocal of the base the same as the number of times of exponent.
Put a multiplication symbol between each and multiply to get the result.

Basic Rules for Power of Numbers

1. Multiplication Rule:

If we have the same base for two or more powers then we can multiply the powers. Now, we will see the rule ie., x^a⋅ x^b=x^a+b, where we multiply two powers and add their exponents.

For Example, 2³. 2⁵ = 2³⁺⁵ = 2⁸

2. Division Rule:

In case the given power of numbers has the same base then we can divide the powers. When we divide powers we will do subtraction with the exponents. The rule is

\(\frac { x^a }{ x^b}\) = x^a-b

For Example, \(\frac { 6⁴ }{ 6²}\) = 6^4-2 = 6²

3. Power of Power Rule:

(x^a)^b=x^ab

4. Power of a Product Rule:

(xy)^a= x^ay^a

Representation of Powers of Number from 1 to 12

Base number	2nd power	3rd power	4th power	5th power
1	1	1	1	1
2	4	8	16	32
3	9	27	81	243
4	16	64	256	1,024
5	25	125	625	3,125
6	36	216	1,296	7,776
7	49	343	2,401	16,807
8	64	512	4,096	32,768
9	81	729	6,561	59,049
10	100	1,000	10,000	100,000
11	121	1,331	14,641	161,051
12	144	1,728	20,736	248,832

Examples of Power of a Number

Example 1.
Find the value of 3⁵.
Solution:
3⁵ = 3 × 3 × 3 × 3 × 3 = 189.

Example 2.
Find the value of 2^-4.
Solution:
2^-4 = Reciprocal of 2⁴ = 1/2⁴ = 1/2×2×2×2 = 1/16.

Example 3.
Find the value of (1024)^1/4.
Solution:
(1024)^1/4
= (8⁴)^1/4
= 8^{4 x 1/4}
= 8

FAQs on Number Powers in Mathematics

1. Can I find Power of a Number online?

Yes, absolutely you can find the power of a number online by using various valid & reliable free math calculators such as OnlineCalculator.Guru, and more.

2. How to write the Power of a Number in Word?

3. What is the Negative power of the number?

A negative power and exponent is represented as the multiplicative inverse of the base, raised to the power which is opposite to the given power. In short, we address the reciprocal of the number and then calculate it like positive exponents. For instance, (1/5)^-3 can be written as (5/1)³ ie., 5³.

4. What is the Fraction power of a number?

The numerator is the power and the denominator is the root in terms of fractinal exponent. For instance, in the variable x ^{\(\frac { a }{ b } \)}, where x, a, and b are real numbers then a is the power and b is the root ie., x^{\(\frac { a }{ b } \)} = ^b√x^a

5. What is the value of power zero of a number?

One is the value of power zero of any non-zero numbers. Whereas Zero is the value for zero to any positive exponent.