Question 69056
{{{4n^x = 4/n^2}}}
First, each side can be divided by 4
{{{n^x = 1 / n^2}}}
Now multiply each side by n^2
{{{n^2*n^x = 1}}}
The left side is similar to something like {{{5^2*5^3 = 5^(2+3)}}}
{{{n^2* n^x = n^(2+x)}}}
{{{n^(2+x) = 1}}}
There is a rule that says "Anything raised to the zero power = 1"
So, stated backwards, "If something raised to an exponent = 1, then that
exponent must be zero"
{{{2 + x = 0}}}
{{{x = -2}}}
check:
{{{4n^x = 4/n^2}}}
{{{4n^(-2) = 4/n^2}}}
multiply both sides by {{{n^2}}}
{{{4n^(-2)*n^2 = 4}}}
{{{4n^(-2+2) = 4}}}
{{{4n^0 = 4}}}
{{{4*1 = 4}}}
OK