Integers As Exponents

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Integers And Exponents

Wondering what are integer exponents? In Mathematical terms, the integer’s exponents are the exponents that must be an integer. An integer’s exponents can be either a positive integer or a negative integer. By the concept, the positive integer exponents explain the number of times the base number must be multiplied by itself. While the negative integer exponents first explain overturn the value of numerator and the denominator and describe multiplying the number by itself for the number of times. Exponents of integers can be bespoken as positive integers, negative integers, or zero.


What Are Positive and Negative Integer Exponents?

An integer is a number that has no fractional portion of which includes the counting numbers such as {1, 2, 3, 4, 5, 6, 7 … n}, zero {0} and the negative of the counting numbers {-5, -4, -3, - 2, -1, 0, 1, 2, 3, 4, 5}. An exponent of a number is the number of times we use that number in a multiplication. Now that you must be well aware of the positive integer exponents and negative integer exponents, let’s get started with reviewing the rules for exponents.


Integer Exponent Rules

  • Rule of Multiplication

By the rule of integer exponent, when we do multiplication of the same bases, we have to add exponents.

a2 • a3 = a2+3 = a5

What is the condition/rule if an exponent is negative? Same thing we need to do i.e. to add exponents.

a7 • a-2 = a7+ (-2) = a5

What is the condition/rule if there is more than one variable? We will do each base individually as given below.

(ab7)(a5b2) = a1+5 b7+2 = a6 b9

What is the condition/rule if there is a coefficient in facing the variable? We will apply the commutative property to reorganize, multiply the coefficients and add exponents

4a3 •- 2a2 = (4 •-2) •(a2 • a3) =- 8a5  


  • Rule of Division

When we divide the same bases, we will require to subtract exponents

a7/a5 = a7-5

What is the condition/rule if the exponent is negative?

-10a7b4/6a-3b = -10/6a7-(-3) b4-(-1) = -5/3 a10b5

What is the condition/rule if there is more than one variable? We will do each base individually as given below.

a7b4/a5b = a7-5 b5-1 = a2b3

What is the condition/rule if there is a coefficient in facing the variable? We will apply the commutative property to reorganize, multiply the coefficients and add exponents.

10a7b4/6a3b2 = 10/6a7-3 b4-1= 5/3 a4b3


  • Raising a Power to a Power

When we raise a power to a power, we will multiply exponents.

(a5)4 = a5•4 = a20

What is the condition/rule if there is more than one variable? We will do each base individually as given below.

(a2b)3 = a2•3 b1•3 = a6b3

What is the condition/rule if there is a coefficient in facing the variable?

(2a4b2)4 = 24 a4•4b2•4 = 16a16b8


  • Negative Exponent Rule

For the expression, y-m = 1/ya

Firstly, write/express with a "top floor" and "bottom floor"

 y-2 = y-2/1 = 1/ y2

Secondly, change the floors if the exponent is "dissatisfied"

 1/y-2 = y2/1 = y2

The exponent is dissatisfied in the denominator; thus, you will move it to the numerator, so it becomes positive.


How to Solve Integer Exponents Using Rules 

make sure to go steadily and meticulously. Here we are providing a shortened version to memorize the rules for exponents.

Multiplication → Add exponents

Division → Subtract exponents

Power to a power → Multiply exponents

Negative → Change "floors"

FAQ (Frequently Asked Questions)

1. What do we understand by exponents in mathematics?

Mathematically, exponents are used to representing repeated multiplication of a number by itself. Writing large numbers in maths at times becomes monotonous. In vast algebraic expressions, they inhabit more space and occupy more time. This issue, in particular, is solved by the use of exponents.

2. What is an example of exponent?

For example, 5 × 5 × 5 can be written as 53. In this example, the exponent is ‘3’ which represents the number of times the given number (value) is multiplied by itself. The number 5 is what we call as the base which is the actual number that is being multiplied. Now let’s say, the speed of light is 200000000 m/s. This can be simply expressed as 2 × 108 m/s (approximate value).

3. What is the process of using exponents called?

This mathematical mechanism of using exponents is known as ‘rising to a power’ in which the exponent is the power. It is important to note that there is a significant difference between exponents and powers.

4. What is the difference between Exponents and Powers?

We are aware that the expression 5 x 5 can be computed; however the expression can also be expressed in a short form that is called as exponents.

 5 × 5 = 52

An algebraic expression that defines repetitive multiplication of the same value is called power. The value 5 is called the base or power and the number 2 is known as an exponent. It is consonant with the number of times the base has functioned as a factor.