Question 862946
<pre>
1. The Zero Exponent Property. This property states that any number (other than
zero itself) raised to the power of zero equals 1. For example,
{{{2^0}}} = 1, {{{x^0=1}}} if x is not zero.  
[However {{{cross(0^0)}}} is not defined.]

2.  The Negative Exponent Property. This property states that any negative
exponent can be converted to a positive by flipping the fraction. For example,
{{{2^(-3)}}} = {{{1/2^3}}} = {{{1/8}}}. 
{{{x^(-7)}}} = {{{1/x^7}}}. 


3. The Property of multiplication when there is a common base. This property
states that when multiplying the same base with different exponents, you can
add the exponents together. For example, 
{{{2^5}}}{{{"×"}}}{{{2^3}}} = {{{2^(5+3)}}} = {{{2^8}}} = {{{256}}}.
{{{y^a}}}{{{"×"}}}{{{y^b}}} = {{{y^(a+b)}}}.

4. The Property of division when there is a common base with different
exponents. This rule states that when dividing the same number with different
exponents, you subtract the exponents. For example
{{{2^5/2^3}}} = {{{2^(5-3)}}} = {{{2^2}}} = 4.
{{{x^9/x^2}}} = {{{x^(9-2)}}} = {{{x^7}}}.

5.  The Property of multiplication when there is a common exponent with
different bases. This property states that when two or more different numbers
with the same exponent are being multiplied, the exponent is only used once.
For example, 
{{{2^3}}}{{{"×"}}}{{{4^3}}} = {{{("2×4")^3}}} = {{{8^3}}} = {{{512}}}.
{{{a^5}}}{{{"×"}}}{{{b^5}}} = {{{(ab)^5}}}.

6.  The Property of division when there is a common exponent with
different bases. This property states that when two or more different numbers
with the same exponent are being divided, the exponent is only used once.
For example,
{{{4^3/2^3}}} = {{{(4/2)^3}}} = {{{2^3}}} = 8.
{{{7^5/9^5}}} = {{{(7/9)^5}}}

7.  The Power to a Power rule. This rule states that when a power is raised to
another power, you multiply the inner exponent by the outer exponent. For
example, 
{{{(2^3)^2}}} = {{{2^("3×2")}}} = {{{2^6}}} = {{{64}}}.
{{{(m^5)^3}}} = {{{m^("5×3")}}} = {{{m^15}}}.

Edwin</pre>