DIVIDING POWERS PROPERTY
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. c12-15 = 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: = 33-5 × 72-3 [Use am/an = am-n]
Step 5: = 3-2 × 7-1
Step 6: = 1/9 × 1/7 [a-m = 1/am.]
Step 7: = 1/63
Quick Summary
- To divide powers with the same base, subtract the exponents.
- Remember that a negative exponent means taking the reciprocal.
🍎 Teacher Insights
Emphasize the importance of having the same base before applying the property. Use numerical examples to illustrate the concept before moving to variables. Review negative exponents thoroughly.🎓 Prerequisites
- Basic arithmetic operations
- Understanding of exponents
- Simplifying fractions
Check Your Knowledge
Q1: Simplify: x7 / x3
Q2: Simplify: 52 / 55
Frequently Asked Questions
Q: What happens when the exponent in the denominator is larger than the exponent in the numerator?
A: You'll get a negative exponent, which means the result is the reciprocal of the base raised to the positive version of that exponent (e.g., a-n = 1/an).
Q: Does this property work if the bases are different?
A: No, the bases must be the same to apply this property.