How to Use the Quotient Rule for Exponents
- 1). Check the base of each exponential expression, or the number beneath the exponent. You can only use the quotient rule to divide exponential expressions that have the same base. So you can divide 4^6 by 4^3, or 3^21 by 3^8, but you can't divide 5^24 by 9^18 because the numbers underneath the exponents are different.
- 2). Subtract the exponent of the divisor -- the number you're dividing by -- from the exponent of the dividend -- the number you're dividing. So if you're dividing 3^6 by 3^2, you would subtract 2 from 6, with a result of 6 - 2 = 4.
- 3). Write the common base both exponential expressions share. Add the result from the previous step as the new exponent. The same base and new exponent, taken together, are your ultimate result. To continue the example, you would have 3^6 / 3^2 = 3^4.
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