Question 404628
{{{(a*b^2*c^(-2))^(-3)}}}
With these problems I like to simplify first. Sometimes the process of simplification causes the zero and/or negative exponents to disappear on their own. After simplifying, if there are still zero or negative exponents, then handle that at the end.<br>
So we'll start with simplifying. The rule for exponents for this type of expression is {{{(p*q)^z = p^z*q^z}}}
Applying this rule to your expression we get:
{{{(a)^(-3)*(b^2)^(-3)*(c^(-2))^(-3)}}}
The rule for a power of a power is to multiply the exponents:
{{{(a)^(-3)*(b^(2*(-3)))*(c^((-2)*(-3)))}}}
which simplifies to:
{{{a^(-3)*b^(-6)*c^6}}}
We're done simplifying. Now we'll address the negative exponents that remain. In general {{{p^(-n) = 1/p^n}}}. Using this pattern on the negative exponents in your expression we get:
{{{(1/a^3)*(1/b^6)*c^6}}}
which simplifies to:
{{{c^6/(a^3*b^6)}}}