Exponent Laws Worksheet Grade 11 with questions and answers PDF Download Find out Exponent Laws Worksheet Grade 11 with questions and answers for the grade and level 11 studies.
Exponent Rules
Exponent rules are those laws that are used for simplifying expressions with exponents. Many arithmetic operations like addition, subtraction, multiplication, and division can be conveniently performed in quick steps using the laws of exponents. These rules also help in simplifying numbers with complex powers involving fractions, decimals, and roots.
Let us learn more about the different rules of exponents, involving different kinds of numbers for the base and exponents.
What are Exponent Rules?
Exponent rules, which are also known as the ‘laws of exponents’ or the ‘properties of exponents’ make the process of simplifying expressions involving exponents easier. These rules are helpful to simplify the expressions that have decimals, fractions, irrational numbers, and negative integers as their exponents.
For example, if we need to solve 34 × 32, we can easily do it using one of the exponent rules which says, am × an = am + n. Using this rule, we will just add the exponents to get the answer, while the base remains the same, that is, 34 × 32 = 34 + 2 = 36. Similarly, expressions with higher values of exponents can be conveniently solved with the help of the exponent rules. Here is the list of exponent rules.
- a0 = 1
- a1 = a
- am × an = am+n
- am / an = am−n
- a−m = 1/am
- (am)n = amn
- (ab)m = ambm
- (a/b)m = am/bm
Seven Laws of Exponents
Video:Algebra Basics: Laws Of Exponents – Math Antics
- Multiplying Powers with same Base.
- Dividing Powers with the same Base.
- Power of a Power.
- Multiplying Powers with the same Exponents.
- Negative Exponents.
- Power with Exponent Zero.
- Fractional Exponent.
Exponent laws with Examples
Exponent laws are a set of rules that govern the manipulation of exponents in mathematical expressions. The four main exponent laws are:
- Product of Powers Law: (a^m)(a^n) = a^(m+n) For example: (2^3)(2^4) = 2^7 = 128
- Quotient of Powers Law: (a^m) / (a^n) = a^(m-n) For example: (8^3) / (8^2) = 8^(3-2) = 8^1 = 8
- Power of a Power Law: (a^m)^n = a^(mn) For example: (2^3)^2 = 2^(32) = 2^6 = 64
- Power of a Product Law: (ab)^n = a^n * b^n For example: (56)^2 = 5^2 * 6^2 = 2536 = 900
It’s important to note that these laws only apply when the bases (the a’s in the examples above) are the same. Also, it’s important to use the correct order of operations when using these laws, to avoid errors.
Exponent Laws Worksheets for Grade 11
FAQs on Exponent Rules
What are Exponent Rules in Math?
Exponent rules are those laws which are used for simplifying expressions with exponents. These laws are also helpful to simplify the expressions that have decimals, fractions, irrational numbers, and negative integers as their exponents. For example, if we need to solve 345 × 347, we can use the exponent rule which says, am × an = am+n, that is, 345 × 347 = 345 + 7 = 3412 . A few rules of exponents are listed as follows:
- Product Rule: am × an = am+n;
- Quotient Rule: am/an = am-n;
- Negative Exponents Rule: a-m = 1/am;
- Power of a Power Rule: (am)n = amn.
What are the 8 Laws of Exponents?
What are the 8 Laws of Exponents?
The 8 laws of exponents can be listed as follows:
- Zero Exponent Law: a0 = 1
- Identity Exponent Law: a1 = a
- Product Law: am × an = am+n
- Quotient Law: am/an = am-n
- Negative Exponents Law: a-m = 1/am
- Power of a Power: (am)n = amn
- Power of a Product: (ab)m = ambm
- Power of a Quotient: (a/b)m = am/bm
What is the Purpose of the Exponent Rules?
The purpose of exponent rules is to simplify the exponential expressions in fewer steps. For example, without using the exponent rules, the expression 23 × 25 is written as (2 × 2 × 2) × (2 × 2 × 2 × 2 × 2) = 28. Now, with the help of exponent rules, this can be simplified in just two steps as 23 × 25 = 2(3 + 5) = 28.
How to Prove the Laws of Exponents?
The exponent laws can be proved easily by expanding the terms. The exponential expression is expanded by writing the base as many times as the power value. The exponent of the form an is written as a × a × a × a × a × …. n times. Further, on multiplying we can obtain the final value of the exponent. For example, let us solve 42 × 44. Using the ‘product law’ of exponents, which says am × an = am+n, we get 42 × 44 = 42 + 4 = 46. This can be expanded and checked as (4 × 4) × (4 × 4 × 4 × 4) = 4096. We know that the value of 46 is also 4096. Hence, the exponent rules can be proved by expanding the given terms.
What are the Exponent Rules when Bases are the same?
When the bases are the same, all the laws of exponents can be applied. For example, to solve 312 ÷ 34, we can apply the ‘Quotient Rule’ of exponents in which the exponents are subtracted. So, 312 ÷ 34 will become 312-4 = 38. Similarly, to solve 49 × 44, we apply the ‘Product Rule’ of exponents in which the exponents are added. This will result in 49+4 = 413.
What are the Exponent Rules when Bases are Different?
When the bases and powers are different, then each term is solved separately and then we move to the further calculation. For example, let us add 42 + 25 = (4 × 4) + (2 × 2 × 2 × 2 × 2) = 16 + 32 = 48. This process is applicable to addition, subtraction, multiplication, and division. In another example, if the expressions with different bases and different powers are multiplied, each term is evaluated separately and then multiplied. For example, 103 × 62 = 1000 × 36 = 36000.
What is the Rule for Zero Exponents?
The rule of zero exponents is a0 = 1. Here, ‘a’, which is the base can be any number other than 0. This law says, “Any number (except 0) raised to 0 is 1.” For example, 50 = 1, x0 = 1 and 230 = 1. However, note that 00 is not defined.
What is the Difference Between Exponents and Powers?
Exponents and powers sometimes are referred to as the same thing. But in general, in the power am, ‘m’ is referred to as an exponent.
Can the Exponent be a Fraction?
Yes, the exponent value can be a fraction. The exponent rule relating to the fraction exponent value is (am)1/n = am/n. This rule is sometimes helpful to simplify and transform a surd into an exponent.