Power Properties
Definition of Power Properties
- Power of a Power Property: This property states that the power of a power can be found by multiplying the exponents.
That is, for a non-zero real number a and two integers m and n, 
.
- Product of Powers Property: This property states that to multiply powers having the same base, add the exponents.
That is, for a real number non-zero a and two integers m and n, 
.
- Quotient of Powers Property: This property states that to divide powers having the same base, subtract the exponents.
That is, for a non-zero real number a and two integers m and n, 
.
- Power of a Product Property: This property states that the power of a product can be obtained by finding the powers of each factor and multiplying them.
That is, for any two non-zero real numbers a and b and any integer m, 
.
- Power of a Quotient Property: This property states that the power of a quotient can be obtained by finding the powers of numerator and denominator and dividing them. That is, for any two non-zero real numbers a and b and any integer m,
.
Examples of Power Properties
- Power of a Power Property:
is the same as 
.
- Product of Powers Property:
is the same as 
.
- Power of a Product Property:
is the same as 
.
- Quotient of Powers Property:
is the same as 
.
- Power of a Quotient Property:
is the same as 
.
Solved Example on Power Properties
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