Since the power of 6 is even, the result will be positive.
\[\frac{{({4}^{6})}^{2}{(-{5}^{2})}^{3}}{{4}^{6}{(-5)}^{2}}\]
Simplify \({5}^{2}\) to \(25\).
\[\frac{{({4}^{6})}^{2}{(-25)}^{3}}{{4}^{6}{(-5)}^{2}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{4}^{12}{(-25)}^{3}}{{4}^{6}{(-5)}^{2}}\]
Since the power of 3 is odd, the result will be negative.
\[\frac{{4}^{12}\times -{25}^{3}}{{4}^{6}{(-5)}^{2}}\]
Simplify \({25}^{3}\) to \(15625\).
\[\frac{{4}^{12}\times -15625}{{4}^{6}{(-5)}^{2}}\]
Simplify negative sign.
\[\frac{-{4}^{12}\times 15625}{{4}^{6}{(-5)}^{2}}\]
Simplify \({4}^{12}\) to \(16777216\).
\[\frac{-16777216\times 15625}{{4}^{6}{(-5)}^{2}}\]
Simplify \(-16777216\times 15625\) to \(-262144000000\).
\[\frac{-262144000000}{{4}^{6}{(-5)}^{2}}\]
Simplify \({4}^{6}\) to \(4096\).
\[\frac{-262144000000}{4096{(-5)}^{2}}\]
Since the power of 2 is even, the result will be positive.
\[\frac{-262144000000}{4096\times {5}^{2}}\]
Simplify \({5}^{2}\) to \(25\).
\[\frac{-262144000000}{4096\times 25}\]
Simplify \(4096\times 25\) to \(102400\).
\[\frac{-262144000000}{102400}\]
Move the negative sign to the left.
\[-\frac{262144000000}{102400}\]
Simplify \(\frac{262144000000}{102400}\) to \(2560000\).
\[-2560000\]
-2560000
