Question 712740
Your error was in squaring {{{(-5m^3n^2)^2}}}. According to one rule of exponents, you raise a single term, like {{{-5m^3n^2}}}, to a power by raising each factor to that power. So according to this rule:
{{{(-5m^3n^2)^2}}}
becomes
{{{(-5)^2(m^3)^2(n^2)^2}}}
Squaring the -5 is easy. To square the powers of m and n we use another rule of exponents: Multiply the exponents! (This is where you went wrong. You apparently squared the 3 and got 9 and squared the 2 and got 4.) So we should get:
{{{25m^6n^4}}}
With {{{(-5m^3n^2)^2}}} properly simplified to {{{25m^6n^4}}} we can now multiply it by {{{-4mn^6}}} giving us:
{{{-100m^7n^10}}}<br>
P.S. Your answer has n to the right power. But it is only a lucky accident that squaring the exponent of 2 (which you should not have done) works out the same as multiplying the exponents of 2 (which you should have done)!<br>