Question

$$\left. \begin{array} { l } { \frac { ( - 4 ) ^ { 25 } \times x ^ { 12 } \times y ^ { 5 } } { ( - 4 ) ^ { 4 } \times x ^ { 5 } \times y ^ { 3 } } } \\ { 5 ) ^ { 11 } - ( 5 ) ^ { 8 x } } \end{array} \right.$$

Answer

$$-2.454109953196*10^15*x^8*y^2$$

Solution


Since the power of 25 is odd, the result will be negative.
\[\frac{-{4}^{25}{x}^{12}{y}^{5}}{{(-4)}^{4}{x}^{5}{y}^{3}}\times 558x\]
Simplify  \({4}^{25}\)  to  \(1.125900\times {10}^{15}\).
\[\frac{-1.125900\times {10}^{15}{x}^{12}{y}^{5}}{{(-4)}^{4}{x}^{5}{y}^{3}}\times 558x\]
Since the power of 4 is even, the result will be positive.
\[\frac{-1.125900\times {10}^{15}{x}^{12}{y}^{5}}{{4}^{4}{x}^{5}{y}^{3}}\times 558x\]
Simplify  \({4}^{4}\)  to  \(256\).
\[\frac{-1.125900\times {10}^{15}{x}^{12}{y}^{5}}{256{x}^{5}{y}^{3}}\times 558x\]
Move the negative sign to the left.
\[-\frac{1.125900\times {10}^{15}{x}^{12}{y}^{5}}{256{x}^{5}{y}^{3}}\times 558x\]
Take out the constants.
\[-\frac{1.125900}{256}\times \frac{{10}^{15}{x}^{12}{y}^{5}}{{x}^{5}{y}^{3}}\times 558x\]
Simplify  \(\frac{1.125900}{256}\)  to  \(0.004398\).
\[-0.004398\times \frac{{10}^{15}{x}^{12}{y}^{5}}{{x}^{5}{y}^{3}}\times 558x\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[-\frac{0.004398\times {10}^{15}{x}^{12}{y}^{5}\times 558x}{{x}^{5}{y}^{3}}\]
Take out the constants.
\[-\frac{(0.004398\times 558){x}^{12}x{y}^{5}\times {10}^{15}}{{x}^{5}{y}^{3}}\]
Simplify  \(0.004398\times 558\)  to  \(2.454110\).
\[-\frac{2.454110{x}^{12}x{y}^{5}\times {10}^{15}}{{x}^{5}{y}^{3}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[-\frac{2.454110{x}^{12+1}{y}^{5}\times {10}^{15}}{{x}^{5}{y}^{3}}\]
Simplify  \(12+1\)  to  \(13\).
\[-\frac{2.454110{x}^{13}{y}^{5}\times {10}^{15}}{{x}^{5}{y}^{3}}\]
Regroup terms.
\[-\frac{2.454110\times {10}^{15}{x}^{13}{y}^{5}}{{x}^{5}{y}^{3}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[-2.454110\times {10}^{15}{x}^{13-5}{y}^{5-3}\]
Simplify  \(13-5\)  to  \(8\).
\[-2.454110\times {10}^{15}{x}^{8}{y}^{5-3}\]
Simplify  \(5-3\)  to  \(2\).
\[-2.454110\times {10}^{15}{x}^{8}{y}^{2}\]