Question 232498
One of the rules for exponents, {{{a^(x*y) = (a^x)^y}}}, allows us to rewrite a factored exponent.<br>
Let's look at you exponent in a factored form. One way would be:
{{{(2/7)^(-2) = (2/7)^(-1*2)}}}
which, according to the property is:
{{{(2/7)^(-2) = (2/7)^(-1*2) = ((2/7)^-1)^2}}}
Rewriting the exponent this way allows us to apply the factors of the exponent one by one. An exponent of -1 means "reciprocal of" so now we have:
{{{(2/7)^(-2) = (2/7)^(-1*2) = ((2/7)^-1)^2 = (7/2)^2 = 49/4}}}<br>
We could also use the other order of factors:
{{{(2/7)^(-2) = (2/7)^(2*(-1)) = ((2/7)^2)^(-1) = (4/49)^(-1) = 49/4}}}