Question 717186
You probably understand the positive exponents:
{{{a*a = a^2}}}, {{{a^2*a=a^3}}}, {{{a^3*a=a^4}}}, {{{a^4*a=a^5}}}, ...<br>
To help us understand negative exponents, let's think about the opposite of the above. Instead of starting with a and repeatedly multiplying by a, think about starting with a high power of a and repeatedly dividing by a:
{{{a^5/a = a^4}}}, {{{a^4/a = a^3}}}, {{{a^3/a = a^2}}}, {{{a^2/a = a^1}}}...
As we did this the exponents kept going down by 1. Now, let's keep going!
{{{a^1/a = 1 = a^0}}} The exponent went down by 1 again!
{{{a^0/a = 1/a = a^(-1)}}} again, the exponent went down by 1
{{{a^(-1)/a = (1/a)/a = 1/a^2 = a^(-2)}}}
etc.