please tell me all the rules of exponents and give me example for each rule .
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Answers
Answer:
Exponent rules
Exponent rules, laws of exponent and examples.
What is an exponent
Exponents rules
Exponents calculator
What is an exponent
The base a raised to the power of n is equal to the multiplication of a, n times:
a n = a × a × ... × a
n times
a is the base and n is the exponent.
Examples
31 = 3
32 = 3 × 3 = 9
33 = 3 × 3 × 3 = 27
34 = 3 × 3 × 3 × 3 = 81
35 = 3 × 3 × 3 × 3 × 3 = 243
Exponents rules and properties
Rule name Rule
Product rules a n ⋅ a m = a n+m
a n ⋅ b n = (a ⋅ b) n
Quotient rules a n / a m = a n-m
a n / b n = (a / b) n
Power rules (bn)m = bn⋅m
bnm = b(nm)
m√(bn) = b n/m
b1/n = n√b
Negative exponents b-n = 1 / bn
Zero rules b0 = 1
0n = 0 , for n>0
One rules b1 = b
1n = 1
Minus one rule
Derivative rule (xn)' = n⋅x n-1
Integral rule ∫ xndx = xn+1/(n+1)+C
Exponents product rules
Product rule with same base
an ⋅ am = an+m
Example:
23 ⋅ 24 = 23+4 = 27 = 2⋅2⋅2⋅2⋅2⋅2⋅2 = 128
Product rule with same exponent
an ⋅ bn = (a ⋅ b)n
Example:
32 ⋅ 42 = (3⋅4)2 = 122 = 12⋅12 = 144
See: Multplying exponents
Exponents quotient rules
Quotient rule with same base
an / am = an-m
Example:
25 / 23 = 25-3 = 22 = 2⋅2 = 4
Quotient rule with same exponent
an / bn = (a / b)n
Example:
43 / 23 = (4/2)3 = 23 = 2⋅2⋅2 = 8
See: Dividing exponents
Exponents power rules
Power rule I
(an) m = a n⋅m
Example:
(23)2 = 23⋅2 = 26 = 2⋅2⋅2⋅2⋅2⋅2 = 64
Power rule II
a nm = a (nm)
Example:
232 = 2(32) = 2(3⋅3) = 29 = 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2 = 512
Power rule with radicals
m√(a n) = a n/m
Example:
2√(26) = 26/2 = 23 = 2⋅2⋅2 = 8
Negative exponents rule
b-n = 1 / bn
Example:
2-3 = 1/23 = 1/(2⋅2⋅2) = 1/8 = 0.125
Answer:
Step-by-step explanation:
Exponents are used to show repeated multiplication of a number by itself. For example, 7 × 7 × 7 can be represented as 73. Here, the exponent is ‘3’ which stands for the number of times the number 7 is multiplied. 7 is the base here which is the actual number that is getting multiplied. So basically exponents of power denotes the number of times a number can be multiplied. If the power is 2, that means the base number is multiplied two times with itself. Some of the examples are:
34 = 3×3×3×3
105 = 10×10×10×10×10
163 = 16 × 16 × 16
Suppose, a number ‘a’ is multiplied by itself n-times, then it is represented as an where a is the base and n is the exponent.
laws of exponents
there are different laws or rules defined for exponents. The important laws of exponents are given below:
am×an = am+n
am/an = am-n
(am)n = amn
an/bn = (a/b)n
a0 = 1
a-m = 1/am
a1n=a−−√n