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,.


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 22×3 = 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:

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

Solution:

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

Translate :

Please provide your email for a free trial as a Teacher or Student. This trial will be valid for the current academic year (2015-16). An email to this address includes the password to login to the full web application. You will also receive other promotional emails as and when such deals become available.

I am a Teacher Student