Dividing Powers (same base) Topic Index | Algebra Index | Regents Exam Prep Center

Rule:

For all numbers x (not zero) and all integers m and n ,

 "This simply means ... when you are dividing, and the bases are the same, you SUBTRACT the exponents." (top exponent subtract bottom exponent)
Consider: ..when in doubt, expand terms

 Observe this rule at work in the following examples:
 1. The bases are the same (both 2's), so the exponents are subtracted.

 2. The bases are the same, so the exponents are subtracted.  Notice how the numbers in front of the bases (7 and 1) are being divided.

 3. The bases are the same (both a's), so the exponents are subtracted. Remember:  top exponent minus bottom exponent.

 4. The bases are the same, so the exponents are subtracted. The numbers in front of the bases are divided.

5.

 The exponents are subtracted for the bases that are the SAME.  The numbers in front, the coefficients, are divided.

 6. Notice what happened to the bases with the same exponents -- they reduced to the number 1.

 7. Remember:  top exponent minus bottom exponent. Remember:  negative exponents can be written as a fraction.

 Topic Index | Algebra Index | Regents Exam Prep Center Created by Donna Roberts