Basic Algebra/Polynomials/Zero and Negative Exponents

Lesson
There are two very important things you need to know when working with Zero Power or Negative Exponents.

First, any number to the Zero Power always equals one. For example (-50)0 = 1

There is one number that CANNOT be raised to the Zero Power, 00 does not exist!

When dealing with Negative Exponents there is a simple trick. Whatever part of a fraction the negative exponent is in, switch it and the exponent becomes positive.

a-2 = 1/a2

1/a-3 = a3

If we have something a little more complicated, we only move things with Negative Exponents. These processes only work with multiplication. If there is addition/subtraction involved, then we are in something a little more complicated than Algebra 1...

(a-2c3)/b-1 = (bc3)/a2

Something like this wouldn't follow the aforementioned rules

(a-2 + b5)/(c6)

This problem would require a little more work: splitting up the fraction and working with both parts individually and having an answer with two fractions instead of one nice one. It's possible but it doesn't flow like the other examples or the practice problems.

Example Problems
(-2)2 = 4. -22 = -4.

Practice Problems
Use  for exponentiation  { (5645848213489487561864756189465548914564751567)0 = { 1_19 }
 * type="{}"}

{ (a-3b4c-1)-2 = { a^6 * c^2 / b^8 (i)|a^6*c^2 / b^8 (i)|a^6c^2 / b^8 (i)|a^6*c^2/b^8 (i)|a^6c^2/b^8 (i)|a^6 * b^(-8) * c^2 (i)|a^6*b^(-8)*c^2 (i)|a^6b^(-8)c^2 (i)|a^6 * b^-8 * c^2 (i)|a^6*b^-8*c^2 (i)|a^6b^-8c^2 (i) _19 }
 * type="{}"}

{ a-8b-2c-1 = { 1 / (a^8 * b^2 * c) (i)|1 / a^8 * b^2 * c (i)|1 / (a^8*b^2*c) (i)|1 / a^8*b^2*c (i)|1 / (a^8b^2c) (i)|1 / a^8b^2c (i)|1/(a^8 * b^2 * c) (i)|1/(a^8*b^2*c) (i)|1/a^8*b^2*c (i)|1/(a^8b^2c) (i)|1/a^8b^2c (i)|1 / a^8 / b^2 / c (i)|1/a^8/b^2/c (i) _19 }
 * type="{}"}

{ a2b-3c4 = { a^2 * c^4 / b^3 (i)|a^2*c^4 / b^3 (i)|a^2c^4 / b^3 (i)|a^2*c^4/b^3 (i)|a^2c^4/b^3 (i) _19 }
 * type="{}"}