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How to Calculate Zero and Negative Exponents

    • 1). Take a look at your problem. Note the base number, or the bigger number, and then note the exponent, or the smaller number that is up and to the right of the base number. It is important that you take the time to fully inspect a math problem before you begin to try and solve it, this will help you to avoid errors in the process of solving the problem.

    • 2). Change the negative exponent to a positive, and then divide 1 by your new positive exponent. If you had the exponent 3^-2, then you would change your exponent to a positive one, 3^2, and then divide one by that exponent, which means that you would now have the fraction, 1/(3^2).

    • 3). Begin to solve the new equation by first calculating the value of your new exponent. With our new equation 1/(3^2), we want to first solve the exponent. Because our base is 3 and our exponent is 2 we are going to multiply 3 by itself once. A good way to remember how many times to multiply a number by itself when solving an exponent is to think of the exponent as telling you how many of the base should appear on your piece of paper. So, for our problem two threes should appear on our piece of paper in order to solve this exponent. So, 3x3=9, our new equation is 1/9.

    • 4). Put your final answer in decimal form if your teacher or the problem instructs you to do so. The best way to do this is to use your calculator to divide 1 by the value your found by solving your exponent. So, in our above problem the decimal answer would be, .11, when rounding to the nearest hundredth.

    Calculating Zero Exponents

    • 1). Take the time to really look at the equation. Whenever you are asked to solve a mathematical problem you should first take stock of the equation. With exponents it is important to look at the base number and the exponent. If the exponent is part of a larger equation then look over the rest of the equation as well as the exponent. This will help you to avoid making errors while attempting to solve math problems.

    • 2). Learn that any number, except zero, to the zero power is equal to 1. The easiest way to solve zero exponents is to simply commit this, The Zero Rule, to memory.

    • 3). Use the rule that (y^x)*(y^z)=y^(x+z) to help you understand how any number other than zero to the zero power equals 1.Lets use this example:3^2=93^0=?(3^2)*(3^0)=3^(2+0)=3^2=9So, if you look at the above equations you can start to see why 3^0=1, but let me clarify it a little more for you using a different way of solving the above equation, (3^2)*(3^0)=9*(3^0) and we know that 9*(3^0) has to equal 3^(2+0) which simplifies to 3^2 and the only way to get that is for 3^0 to equal 1.

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