Question 187783
{{{(3x)^(-2)/(4x^2)^(-2)}}} Start with the given expression.



{{{((3x)/(4x^2))^(-2)}}} Since both the numerator and denominator have the same negative exponent, this means that we can write the entire expression with one negative exponent.



{{{((4x^2)/(3x))^(2)}}} Flip the fraction to make the exponent positive.



{{{((4x^cross(2))/(3*cross(x)))^(2)}}} Cancel out the common terms.



{{{((4x)/(3))^(2)}}} Simplify



{{{(4x)^2/(3)^2}}} Apply the outer exponent to each term.



{{{(16x^2)/(9)}}} Square each term.



So {{{(3x)^(-2)/(4x^2)^(-2)=(16x^2)/(9)}}} as long as {{{x<>0}}}