Question

$$\frac{(-4)^{25}\times x^{12}\times y^{5}}{(-4)^{4}\times x^{5}\times y^{3}}$$

Answer

$$-0.0043980465111039*10^15*x^7*y^2$$

Solution


Since the power of 25 is odd, the result will be negative.
\[\frac{-{4}^{25}{x}^{12}{y}^{5}}{{(-4)}^{4}{x}^{5}{y}^{3}}\]
Simplify  \({4}^{25}\)  to  \(1.125900\times {10}^{15}\).
\[\frac{-1.125900\times {10}^{15}{x}^{12}{y}^{5}}{{(-4)}^{4}{x}^{5}{y}^{3}}\]
Since the power of 4 is even, the result will be positive.
\[\frac{-1.125900\times {10}^{15}{x}^{12}{y}^{5}}{{4}^{4}{x}^{5}{y}^{3}}\]
Simplify  \({4}^{4}\)  to  \(256\).
\[\frac{-1.125900\times {10}^{15}{x}^{12}{y}^{5}}{256{x}^{5}{y}^{3}}\]
Move the negative sign to the left.
\[-\frac{1.125900\times {10}^{15}{x}^{12}{y}^{5}}{256{x}^{5}{y}^{3}}\]
Take out the constants.
\[-\frac{1.125900}{256}\times \frac{{10}^{15}{x}^{12}{y}^{5}}{{x}^{5}{y}^{3}}\]
Simplify  \(\frac{1.125900}{256}\)  to  \(0.004398\).
\[-0.004398\times \frac{{10}^{15}{x}^{12}{y}^{5}}{{x}^{5}{y}^{3}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[-0.004398\times {10}^{15}{x}^{12-5}{y}^{5-3}\]
Simplify  \(12-5\)  to  \(7\).
\[-0.004398\times {10}^{15}{x}^{7}{y}^{5-3}\]
Simplify  \(5-3\)  to  \(2\).
\[-0.004398\times {10}^{15}{x}^{7}{y}^{2}\]