To divide terms with like bases, keep the base and subtract the exponents. Mathematicians describe this rule as x^m/x^n = x^m-n. For example, to simplify the expression 5^10/5^3, keep 5 as the base and subtract 3 from 10 to get a new exponent of 7. You may also have a negative number as an exponent. For instance, if you reverse the expression to 5^3/5^10, the answer is 5^-7.
You can only divide exponents if they have the same base. For instance, x^2/y^2 is already in its simplest form. To understand why, examine the expression 5^2/4^2. This is the same as 25/16, which equals 1.5625. If you try to subtract the exponents, you are left with 5^0/4^0, which simplifies to 1/1, or 1. Do not be fooled by bases that have identical exponents. Although they may look the same, they are unrelated.
Exponents can be divided as well as terms. These are called fractional exponents. 9^1/2 is an exponential equation when the exponent, 1, is divided by 2. To simplify an exponential fraction, raise the base to the power of the numerator and take this answer by the root of the denominator. For example, 9^1/2 equals √(9^1), which is 3.
When you subtract the exponents to solve a division problem and the answer is 1 or 0, special rules apply. Any number raised to the power of 1 equals itself. Therefore, if you divide 4^4 by 4^3, the answer is 4. An exponent of 1 is never expressed. If the exponent is 0, the simplified expression equals 1, regardless of the value of the base. For example, 1^0, 2^0 and 3^0 all equal 1.