#Simplify negative exponents how to#

If we wanted to simplify 3 -2 we would take the reciprocal of 3. Another way to think about this is by stating that we will drag the base and exponent across the fraction bar and make the exponent positive. When we want to simplify with negative exponents, we take the reciprocal of the base and make the exponent positive. This was just to give you an understanding of where our simplified result comes from. Obviously, we will not be going through all this division each time we need to simplify with negative exponents. Now we can simplify the complex fraction by. Divide by the base (3) each time we reduce the exponent by 1: We can write any term with a negative exponent without a negative exponent by taking the reciprocal - e.g. 1 would be divided by 3, and could be written as 1/3:Īs we continue to decrease our exponent by 1, we continue the same process.

What happens if we continue and decrease the exponent by 1 to (-1)? We would continue the pattern. Therefore, we say zero raised to the power of zero is undefined. We can't divide 0 by 0, this is undefined. If we try to raise zero to the power of zero, we will have a problem. We can state that any non-zero number raised to the power of zero is 1. So what happens when we get to 3 0? We continue the same pattern. If we want 3 1, we can divide 9 by 3 to obtain 3. If we move to 3 2, we can divide 27 by 3 to obtain 9. When we go from 3 4 (81) to 3 3 (27), we could just divide 81 by 3 to obtain 27. This is because we are removing a factor of 3 when we decrease the exponent by 1. What is the value of 3 to the power of (-4)? To understand negative exponents, let's think about a pattern:Įach time we reduce our exponent by 1, we divide by our base of 3. with negative exponents are moved to the bottom of the fraction.

#Simplify negative exponents how to#

What happens if we see something such as: This lesson will explain how to simplify the negative exponents in problems like the. Negative Exponents & the Power of Zero Up to this point, we have only dealt with whole-number exponents larger than 1. In this lesson, we will expand on our knowledge of the rules of exponents and learn about negative exponents, the power of zero, and the quotient rule for exponents. In our last lesson, we learned about the power rules and product rule for exponents.