In mathematics, the exponent is described as a number that says how many times to use that specified number in a multiplication operation. It can be seen as a small number written to the right-hand side and above the base number. For example,
In this, the exponent "2" says to use the 3 two times in a multiplication. Similarly, in another example,
Here, the exponent "3" says to use the 4 three times in a multiplication. Exponents can also be called index or power based on the context.
In the RD Sharma Solutions for Class 7 Maths Chapter 6 exponents, students are taught how to find the value of a given number in the exponential form. One alternative method of expressing numbers in exponential notation. Similarly, another very specific example of exponential numbers is the scientific notation, where 10 is almost always used as the base number. So, 103 means 10 * 10 * 10 * 10, whereas 10-4 is the notation for the reciprocal of 104, such as 1/10000. This is also called the standard form.
Furthermore, students also get familiarised with a concept called laws of exponents. Some common laws of exponents are Zero Power Rule, Quotient with Same Base, Powers with Same Base, Fractional Exponent Rule, Negative Exponent Rule, Power of a Power, Product of a Power, Quotient of a Power. In Class 7 Maths Chapter 6 exponents, students learn how to use the exponents in expressing large numbers in a standard form. A standard form is a concept in which any number can be expressed as a decimal between 1.0 and 10.0, including the multiplication by a power of 10. For example, let us take 7500, we can express this number in many different ways;
7500 = 75 * 100 = 75 * 102
7500 = 750 * 10 = 750 * 101
7500 = 7.5 * 1000 = 7.5 * 103
7500 = 0.75 * 10000 = 0.75 * 104
Thus, all the numbers mentioned above are the representation of the number 7500 in exponent form. But its standard form is 7500, and it can be expressed as a number between 1 and 10. Moreover, expanded exponential form has also been taught to the students, which is a way of writing numbers to see the math value of individual digits.