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Exponents are also known as powers. They are values that show how many times a base number needs to be multiplied by itself. The number being raised by the power is known as the base, while the superscript number above is the given exponent or power. The power of two can also be known as “squared,” and the power of three can be known as “cubed.” These terms are often used when finding the area or volume of different shapes. When the power of an exponent is negative, it is known as negative exponents. Exponents are a way to simplify equations so that it becomes easier to read and understand. Exponents Are helpful when students are dealing with variables such as ‘𝒙’ and ‘𝑦.’
There are seven rules of Exponents, or laws of exponents, that students need to learn and master. Exponent rule helps students solve different types of mathematical equations and also helps them explore how to add, subtract, multiply and divide the exponents. Cuemath is an online learning platform that can help you explore exponents in the most engaging way. Cuemath resources and study material keeps students way ahead by boosting their logical and reasoning skills.
Let us go over each of these rules in detail as it plays an important role in solving and understanding exponent-based equations and problems.
In Exponents, when multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the answer. 22 × 25 =?Since the base values are both two, keep them the same and then add the exponents (2 + 5) together. 22× 25 = 27.
Multiplication and division are opposites of each other. The quotient rule here acts as the opposite of the product rule in Exponents. When dividing two bases of the same given value, keep the base the same and then subtract the exponent values. 56 ÷ 53 =? Both the bases in this respective equation are five, which means they stay the same. Then, take the exponents and subtract the denominator from the dividend. 55 ÷ 53 = 53. Then students have to simplify the equation if needed.
This rule in Exponents shows students how to solve equations when power is being raised by another power. (𝒙3)Three =? In these equations, students have to multiply the exponents together and keep the given base the same. (𝒙3)3 = 𝒙9. This rule makes the students understand the working of power and its need.
When any base is being multiplied by an exponent, allocate the exponent to each part of the given base. (ab)Three =? In this equation, the power of three has to be distributed to both the a and the b variables. (ab)3 = a3b3. This rule of products is used if there are exponents attached to the base as well.
When any base is being multiplied by an exponent, allocate the exponent to each part of the given base. (ab)Three =? In this equation, the power of three has to be distributed to both the a and the b variables. (ab)3 = a3b3. This rule of products is used if there are exponents attached to the base as well.
A quotient simply means that you’re dividing two quantities together. In this rule of exponents, you are raising a quotient by the given power. Like the power of a product rule mentioned above, the exponent needs to be distributed to all the values within the brackets it is attached to. (a/b)Four = ? in this equation, raise both the variables within the brackets by the power of four that is mentioned.
In this rule, it is said that any base raised to the power of zero is equal to one. This rule is the simplest to follow and understand.
In Exponents, when there is a number that a negative exponent is raising in an equation, upturn it into a reciprocal to turn the exponent into positive. Students should not use the negative exponent to turn the base into a negative.
Exponents are very easy and simple to understand with the help of these seven rules. Students should memorize and understand these rules effectively in order to master the concepts of exponents.
