Exponents & Laws of Exponents

There are various exponent laws in mathematics. Exponent rules are used to solve many mathematical problems that involve repeated multiplication processes. The laws of exponents simplify multiplication and division operations and make it easier to solve problems. In this article, we will go over the six most important laws of exponents, along with numerous solved examples. 

What are Exponents?

Exponents are used to represent the repeated multiplication of a single number. For example, 7 × 7 × 7 can be written as. The exponent, in this case, is ‘3,’ which represents the number of times the number 7 is multiplied. The base number here is 7, which is the number that is being multiplied. Exponents or powers, in essence, denote the number of times a number can be multiplied. If the power is 2, it means that the base number has been multiplied twice.
Exponents are necessary because it is difficult to write products in which a number is repeated many times by itself without them. For example, it is much easier to write 57 than it is to write 5 × 5 × 5 × 5 × 5 × 5 × 5.
Exponents and powers are not distinguished. Exponents are also known as powers and adding an exponent to something is equivalent to raising it to the level of power. Exponents are simply a shortcut for indicating multiples of the same thing.
When you see an exponential function, the larger number is at the bottom, followed by a small number in the upper right-hand corner. The large number at the bottom is referred to as the “base,” while the small number in the corner is referred to as the “exponent.” The exponent is always added to the base. 

What are Laws of Exponents?

Exponent rules are laws that are used to simplify exponential expressions. Many arithmetic operations, such as addition, subtraction, multiplication, and division, can be performed quickly and easily using the laws of exponents. These rules can also be used to simplify numbers with complex powers that involve fractions, decimals, and roots. 

Laws of Exponents

The exponent rules are as follows: 0 rule, 1 rule, exponent power rule, negative exponent rule, product rule, and quotient rule. They are the rules that you use to simplify and solve exponent problems. And, because exponents have their own set of operations, you should apply the rules in the order I just listed when simplifying exponent problems.
When the exponent is zero, the 0 rule is used. According to the rule, anything raised to the power of 0 equals one. 0 is the only exception (0, an indeterminate form).
Exponents’ Product Property – Exponents’ product property is used to multiply expressions with the same bases. “To multiply two expressions with the same base, add the exponents while keeping the base the same,” says this property. This rule requires you to add exponents with the same base. 
Exponents’ Quotient Property – To divide expressions with the same bases, the quotient property of exponents is used. “To divide two expressions with the same base, subtract the exponents while keeping the base constant,” says this property. This is useful for solving expressions without performing the division process. The only requirement is that the bases of the two expressions be the same. 
Exponents’ Zero Property- When the exponent of an expression is zero, the zero property of exponents is applied. “Any number (other than 0) raised to 0 is 1,” says this property. It is worth noting that the value 00 is not defined. This will assist us in understanding that, regardless of the base, the value for a zero exponent is always equal to 1.

To know more about the laws of exponents, you can visit the Cuemath website.