Difference Between Power And Exponent, Definition, Important Topics For JEE 2024
Difference Between Power and Exponent : Read everything you need to know about the important terms used in Algebra. Learn the difference between power and exponent.
Shrivastav 18 Jan, 2024
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Difference Between Power And Exponent : Exponents and powers are useful tools in mathematics, particularly algebra, for efficiently rewriting lengthy multiplication problems. One of the important fields of mathematics that focuses primarily on the concept of number theory is algebra. It is also known as the study of mathematical symbols.
The difference between power and exponent is a very small point that is often misunderstood. The difference between power and exponent is quite thin. Power is the term used to represent the repeated multiplication of a factor; the exponent is the value increased to that base factor. This is the primary difference between power and exponent. For example, 3 2 is the power that has 3 as the base and 2 as the exponent. In this post. We will learn the difference between power and exponent . Achieve JEE excellence with PW JEE Online Course . Join now to fulfill your engineering dreams. Before we discuss the difference between power and exponent, let’s first discuss their meanings and their characteristics.Definition of Power
In mathematics, increasing a base number to the exponent is referred to as "power." It indicates that "base number" and "exponent" are the two fundamental components of powers. A base number is a number that has been multiplied by itself. On the other hand, the exponent shows how many times the base number has been multiplied. Power is just a number represented with exponents. It suggests multiplying the same factor more than once.Definition of Exponent
Small numbers that are positioned to the right of base numbers are known as exponents in mathematics. Numbers, variables, or constants can all be exponents. Exponents signify how many times the base number needs to be multiplied itself. Typically, exponents are used to representing huge numbers. We call this increase to a power process. We might see exponents in various scientific notations to express the high numbers as the powers of 10. An example would be the exponent 1.50 × 108 km, which represents the distance between the Earth and the sun.Key Difference Between Power and Exponent
The following points in the table make it easy to tell the difference between power and exponent:| Difference Between Power and Exponent | ||
| Particulars | Exponent | Power |
| Definition | Refers to the number of times a number is used in a multiplication. | Can be defined as a number being multiplied by itself a specific number of times. |
| Role in Expression | The number to which a number is raised for defining its power as a whole expression. | The whole expression including the base and the exponent. No specific position. |
| Representation | Always written as a superscript of the base number. | Consists of two parts: the base and the exponent. No specific position. |
| Components | Consists of only the superscript number. | Comprises both the base and the exponent. |
| Example | 5 6 = 5×5×5×5×5×5 The exponent of this equation is 6, meaning that it indicates how many times 5 must be multiplied by itself. | 5 4 = 5×5×5×5 The expression's base number, 5, must be multiplied by itself four times in order to get the desired result, 54=625 is sometimes expressed as "five to the fourth power" or the "fourth power of five." |
Laws of Exponents
Exponents follow a set of rules when applied to mathematical equations, which makes a variety of equations easy to understand and solve.| Laws of Exponents | ||
| Exponent Rule | Explanation | Example |
| Reciprocal Law or Negative Exponent Rule | If an exponent is negative, the reciprocal law allows us to change the sign of the exponent by taking the reciprocal of the number. | a -x =1/a x |
| Zero Exponent Rule | Any number raised to the exponent 0 equals 1. | A 0= =1 |
| Product Law of Exponents | When multiplying expressions with the same base, add the exponents. | a n ⋅ a m =a n+m |
| Quotient Law of Exponents | When dividing two powers with the same base, subtract the exponents. | aman=an−m |
| Power of a Power Law | The power of a power is obtained by multiplying the exponents. | (a n ) m =a nm |
| Power of Product Rule | The power of a product is found by applying the exponent to each factor separately. | (BC) n =B n ⋅ C n |
| Power of Quotient Rule | The power of a quotient involves applying the exponent to the numerator and denominator separately. | (x/y) n =x n /y n |
Difference Between Power and Exponent FAQs
Q.1. Are power and exponent the same thing?
Ans. Power in mathematics is defined as a base number raised to the exponent, where the exponent indicates the number of times the same base number is multiplied, and the base number is the factor multiplied by itself.
Q.2. What is algebra and its uses?
Ans. The area of mathematics known as algebra helps in converting problems or situations into mathematical statements.
Q.3. Who created math?
Ans. The Sumerians, who established the first civilization in Mesopotamia, are the people who left the oldest written records of mathematics.
Q.4. In exponent and power, how many laws are there?
Ans. In exponent and power, there are eight laws in all.
Q.5: What practical uses do powers and exponents have?
Ans. In certain scientific applications, like the Richter or pH scale, powers and exponents are highly helpful for taking measurements and writing both very tiny and very big values.
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