The exponent calculator is pretty straight-forward. Input the base, then the exponent, and get the answer below. It also handles negative exponents. This is the same operation that you might see typed out as "X ^ Y," where X is the base and Y is the exponent. An exponent is an operation in which the exponent designated the number of times the base is multiplied times itself. Some examples:
•3 ^ 4 = 3 * 3 * 3 * 3 = 81•4 ^ 3 = 4 * 4 * 4 = 64•2 ^ 3 = 2 * 2 * 2 = 8•2 ^ -4 = 0.5 * 0.5 * 0.5 * 0.5 = 0.0625•4 ^ -1 = 0.25
When we take the negative exponent of a number, that's the same thing as multiplying the reciprocal of the base times itself that many loops. Thus 4 times itself "negative one times" means the fraction 1/4th, or 0.25.
Funny things happen at the edge cases. For instance, any integer base to the exponent of -1 yields 1. Zero raised to the negative exponent of any value is infinity, but actually it's considered one of those undefined problems related to dividing by zero. Finally, one tricky aspect is negative numbers raised to positive exponents. Check out this sequence:
•-2 ^ 2 = 4•-2 ^ 3 = -8•-2 ^ 4 = 16•-2 ^ 5 = -32
The rule in multiplication is that like signs produce a positive result, opposite signs produce a negative result. So look at " -2 ^ 3":
•-2 ^ 3 = -2 * -2 * -2•-2 * -2 = 4•4 * -2 = -8
When the exponent is even, the result is positive, but when the exponent is odd, the result is negative. The same even / odd pattern occurs with negative bases raised to negative exponents, producing alternate positive and negative results.
Practical Applications of Exponents
Exponents come up all the time in various science fields. Take biology: Say we have a Petri dish of bacteria which reproduce through fusion (splitting in two), taking an hour to do so. Starting with 2 bacteria, in ten hours we get over a thousand. Exponential growth is very important to understand because its explosive rise always indicates something unsustainable; our bacteria experiment would level off after a while because there was no more room in the dish, for instance.
Exponents are fun to play with and chart, using graphing calculators and the like. They also come in handy for applications ranging from engineering to physics.