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, (am)n = amn.

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, am an = am+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 Properties .

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, (ab)m = am bm.

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,Power_Properties.

Video Examples: Power of a Power Property


Example of Power Properties

    In the above figure, the letter R is on the top.
  • Power of a Power Property: (22)3 = 43 = 64 is the same as 223 = 26 = 64.
  • Product of Powers Property: 22 25 = 4 32 = 128 is the same as 22+5 = 27 = 128.
  • Power of a Product Property: (3 4)2 = 122 = 144 is the same as 32 42 = 9 16 = 144.
  • Quotient of Powers Property:Power Properties is the same as 54-3 = 51 = 5.
  • Power of a Quotient Property: Power Properties is the same asPower Properties .

Solved Example on Power Properties

Ques: Evaluate:  example of  Power Properties

    Choices:
    A. 823,543
    B. 16,807
    C. 2,401
    D. 117,649
    Correct Answer: B

Solution:

    Step 1:  example of  Power Properties [To divide powers with same base, subtract their exponents.]
    Step 2: = 75 = 16,807 [Simplify.]
    Step 3: So, example of  Power Properties .