Definition Of Dividing Powers Property

To divide the bases with powers, subtract the power of the denominator from that of the numerator i.e. .

Example of Dividing Powers Property

To divide c¹²/c¹⁵, subtract the powers.
i.e. c^12-15 = c^-3 = 1/c³

Video Examples: Division Of Terms With Same Exponents Example-1 / Laws Of Exponents / Power Of A Quotient Property
 

Solved Example on Dividing Powers Property

Ques: Simplify: (27/243) ÷ (343/49)

Choices:

A. 1/63
B. 21
C. 63
D. 27
Correct Answer: A

Solution:

Step 1: (27/243) ÷ (343/49) [Original expression.] 
Step 2: = 3³/3⁵ ÷ 7³/7² [Write in the exponential form.]
Step 3: = 3³/3⁵ × 7²/7³
Step 4: = 3^3-5 × 7^2-3 [Use a^m/aⁿ = a^m-n]
Step 5: = 3^-2 × 7^-1
Step 6: = 1/9 × 1/7 [a^-m = 1/a^m.]
Step 7: = 1/63

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