list all the laws of exponents with examples
Answers
Step-by-step explanation:
Rules of Exponents With Examples
As discussed earlier, there are majorly six laws or rules defined for exponents. In the table below, all the laws are represented.
am.an=am+n
(am)n = amn
(ab)n = an bn
(a/b)n = an/bn
am/an = am-n
am/an = 1/an-m
Now let us discuss all the laws one by one with examples here.
Also, read:
An Introduction To Exponents
Exponents And Powers for Class 7
Exponents And Powers For Class 8
Product With the Same Bases
As per this law, for any non-zero term a,
am×an = am+n
where m and n are real numbers.
Example 1: What is the simplification of 55 × 51 ?
Solution: 55 × 51 = 55+1 = 56
Example 2: What is the simplification of (−6)-4 × (−6)-7?
Solution: (−6)-4 × (−6)-7 = (-6)-4-7 = (-6)-11
Note: We can state that the law is applicable for negative terms also. Therefore the term m and n can be any integer.
Quotient with Same Bases
As per this rule,
am/an = am-n
where a is a non-zero term and m and n are integers.
Example 3: Find the value when 10-5 is divided by 10-3.
Solution: As per the question;
10-5/10-3
= 10-5-(-)3
= 10-5+3
= 10-2
= 1/100
Power Raised to a Power
According to this law, if ‘a’ is the base, then the power raised to the power of base ‘a’ gives the product of the powers raised to the base ‘a’, such as;
(am)n = amn
where a is a non-zero term and m and n are integers.
Example 4: Express 83 as a power with base 2.
Solution: We have, 2×2×2 = 8 = 23
Therefore, 83= (23)3 = 29
Product to a Power
As per this rule, for two or more different bases, if the power is same, then;
an bn = (ab)n
where a is a non-zero term and n is the integer.
Example 5: Simplify and write the exponential form of: 1/8 x 5-3
Solution: We can write, 1/8 = 2-3
Therefore, 2-3 x 5-3 = (2 × 5)-3 = 10-3
Quotient to a Power
As per this law, the fraction of two different bases with the same power is represented as;
an/bn = (a/b)n
where a and b are non-zero terms and n is an integer.
Example 6: Simplify the expression and find the value:153/53
Solution: We can write the given expression as;
(15/5)3= 33 = 27
Zero Power
According to this rule, when the power of any integer is zero, then its value is equal to 1, such as;
a0 = 1
where ‘a’ is any non-zero term.
Example 7: What is the value of 50 + 22 + 40 + 71 – 31 ?
Solution: 50 + 22 + 40 + 71 – 31 = 1+4+1+7-3= 10