7 Basic Rules for Exponents

Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, base number is b and n is exponent. Now, we will share to you about the basic rules of exponetitation. There are 7 basic rules in exponentitation, such as:

Multiplication rules of exponents with the same basic number
Division rules of exponetitaion with the same basic mumber
Exponents rule on exponent number
Exponents rule of multiplication two number
Exponents rule of division two number
Rule of negative exponents number
Exponents rule of fractional number

1. Multiplication rules of exponents with the same basic number

a^p x a^q = a^p+q

Information:
a : number
p and q : exponent of the number

Example :
What is the result of 5² x 5³ ?

Answer:
a = 5
p = 2
q = 3

a^p x a^q = a^(p+q)
5² x 5³ = 5⁽²⁺³⁾
5² x 5³ = 5⁵

2. Division rules of exponetitaion with the same basic mumber

a^p : a^q = a^p-q

Information:
a : number
p and q : exponent of the number

Example :
What is the result of 5³ : 5² ?

Answer:

a = 5

p = 3

q = 2

a^p : a^q = a^(p+q)
5³ : 5² = 5^(3-2)
5³ : 5² = 5¹

3. Exponents rule on exponent number

(a^p)^q = a^{(p x q)}

Information:
a : number
p and q : exponent of the number

Example :
What is the result of (5²)³ ?

Answer:
a = 5
p = 2
q = 3

(a^p)^q = a^{(p x q)}
(5²)³ = 5^{(2 x 3)}
(5²)³ = 5⁶

4. Exponents rule of multiplication two number

(a x b)^p = a^p x b^p

Information:
a and b : number
p : exponent of the number

Example :
What is the result of (4 x 5)² ?

Answer:
a = 4
b = 5
p = 2

(a x b)^p = a^p x b^p
(4 x 5)² = 4² x 5²
(4 x 5)² = 16 x 25

(4 x 5)² = 400

5. Exponents rule of division two number

(a : b)^p = a^p : b^p

Information:
a and b : number
p : exponent of the number

Example :
What is the result of (4 : 2)² ?

Answer:
a = 4
b = 2
p = 2

(a : b)^p = a^p : b^p
(4 : 2)² = 4² : 2²
(4 : 2)² = 16 : 4

(4 : 2)² = 4

6. Rule of negative exponents number

a^-p = 1/a^p

Information:
a : number
p : exponent of the number

Example :
What is the result of 2^-2 ?

Answer:
a = 2
p = -2

a^-p = 1/a^p
2^-2 = 1/2²
2^-2 = 1/4

7. Exponents rule of fractional number

a^p/q = ^q√a^p

Information:
a : number
p and q : exponent of the number

Example :
What is the result of 2^4/2 ?

Answer:
a = 2
p = 4
q = 2

a^p/q = ^q√a^p
2^4/2 = ²√2⁴
2^4/2 = ²√16
2^4/2 = 4

The end of this article. Sorry if we made a mistake.

Finaly I want to say wassalamualaikum wr. wb.

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