Integers As Exponents

What are Integer Exponents?

Integer exponents, mathematically refer to those exponents that should be integers whether positive integers or negative integers. The positive integer exponents denote the number of times a number should be multiplied by itself. The negative exponents as a rule need to first be flipped and then multiplied.


What are Integers?

Did you know that the word integer is derived from the Latin word integer meaning whole? Integers refer to a number that can be represented as a non-fraction. That is numbers that can be written without a fractional component are defined as an integer.

Net gears can be positive or negative.Examples of integer are- 1, 4, 9, -7, -66, etc.


What are Exponents?

Exponents represent the mathematical operation of exponentiation. Exponents of a number show how many times a number should be used in multiplication whether with itself or with other numbers.

For example, 23, where 3 is the exponent and means that two should be multiplied with itself three times.


Integers and Exponents

Simply put, all integers can be exponents-whether positive or negative. Exponents denote the number of times a base number should be multiplied whether with itself or with another number.

For example, the expression 5 × 5 can also be written as 52. The integer here is both 2 and 5 but the exponent is 2. The exponent 2 here denotes that 5 has to be multiplied twice with itself.

Similarly, 43 stands for 4 × 4 × 4 HD shows that 4 should be multiplied with itself three times.


Integer Exponents Rule

Seven major exponents rules are the answer to the question-“how to solve integer exponents”. These rules are all-encompassing in terms of mathematical operations such as addition, multiplication, division, etc.


Let us understand these rules properly:

1. Product of Powers Rule

When two bases of the same number are to be multiplied, add the exponents while keeping the base number the same.

For example- 32 × 34 = 32+4

= 36

= 3 × 3 × 3 × 3 × 3 × 3

= 729


2. Quotient of Powers Rule

When two bases with the same number are being divided, subtract the exponents while keeping the base the same.

For example-  46 divided by 42 = 46-2

= 44

= 4 × 4 × 4 × 4

= 256


3. Power of a Power Rule

When an exponent is being raised to another exponent, multiple the two exponents and keep the base the same.

For example- (52)3 = 56

= 5 × 5 × 5 × 5 × 5 × 5

= 15,625


4. Power of a Product Rule

When two bases are being multiplied by the same exponent, distribute the exponent to each of the bases.

For example- (41 × 51)2 = 42 × 52

= 16 × 25

= 400


5. Power of a Quotient Rule

When a power is raised to a quotient-distribute it evenly to both the denominator and numerator.

For example- (⅘)2 = 42/5

= 16/25


6. Zero Power Rule

Any base raised to the power of zero is equal to one.

For example- 30 = 1


7. Negativity Content Rule

When any base is raised to a negative exponent, turn the number into a fraction and then make it reciprocal.

For example- 3-2 = 1/32

The idea behind this rule is to convert the negative exponent to make them into positive ones.


How to Solve Integer Exponents?

Solving integer exponents can be a very easy task if the student is clear with the basics of this concept. As we have explained above Integer exponents are exponents that stand for an integer both negative and positive and denote the number of times the base number should be multiplied with itself or with another number.

Seven rules govern the solving process and all of them have been mentioned by us above. It is through the use of these rules that integer exponent questions can be solved.


Let us look at the general steps of solving such questions-

  • Step 1. Carefully look at the question.

  • Step 2. Discern which of the seven formulas would be suitable.

  • Step 3. Use the chosen formula.

  • Step 4. Write the answer clearly.

  • Step 5. Recheck the process and the final answer.

The entire process of employing one of the formulas, finding the answer, and then re-checking would make sure that there is no scope for mistakes and if done they can be corrected. Such a strategy would help make you score high marks and avoid silly mistakes.

FAQs (Frequently Asked Questions)

Q1. How to Solve Integer Exponents Questions to Score Full Marks?

Ans. The best way to Solve integer exponent questions is to first understand the basics of the topic. The second step would be to be thorough with all of the formulas and practice each formula an adequate number of times.


To ensure that you score full marks you should always recheck your answers, the formula used, and the calculation. This will help you avoid silly mistakes and ensure that you will score full marks. You just need to keep yourself in focus and then you can easily get through this chapter.

Q2. How to do Integer Exponents?

Ans. The quickest way to solve integer exponent questions is to use one of the seven formulas mentioned. After properly looking at the question choose one of the formulas or sometimes multiple formulas to solve the question.

Always re-check the formula used as well as the calculation to avoid silly mistakes.

Q3. How Many Questions Should One Practice on Integer Exponents?

Ans. There is no definite number of questions that one should strive to solve. Loosely speaking, you should first understand the basics and the formula and then practice questions on each formula.


Practice makes perfect and so you should try to do as many questions and as many varieties of questions as possible. Practice even harder when exams are near.

Q4. How are Exponents and Powers Used in Real Life?

Ans. Exponents and powers are used in all technological worlds, their use can be seen at research departments for measuring pH scale. They are also used to measure the strength of magnitude, earthquake, and logarithmic scale.