Solve (3/2)^2*9*(-2/3)^202

$$( \frac { 3 } { 2 } ) ^ { 2 \times 9 } \times ( - \frac { 2 } { 3 } ) ^ { 202 }$$

Evaluate

$$\frac{24519928653854221733733552434404946937899825954937634816}{6170365191715177779482467945369860501784408913594010934644126825341528124785676079587681}\approx 3.973821304 \cdot 10^{-33}$$

Solution Steps

Multiply 2 and 9 to get 18.

$$\left(\frac{3}{2}\right)^{18}\left(-\frac{2}{3}\right)^{202}$$

Calculate \frac{3}{2} to the power of 18 and get \frac{387420489}{262144}.

$$\frac{387420489}{262144}\left(-\frac{2}{3}\right)^{202}$$

Calculate -\frac{2}{3} to the power of 202 and get \frac{6427752177035961102167848369364650410088811975131171341205504}{2390525899882872924049031898322016641463101073880550463771174655651832418111719646949462291396009}.

$$\frac{387420489}{262144}\times \frac{6427752177035961102167848369364650410088811975131171341205504}{2390525899882872924049031898322016641463101073880550463771174655651832418111719646949462291396009}$$

Multiply \frac{387420489}{262144} and \frac{6427752177035961102167848369364650410088811975131171341205504}{2390525899882872924049031898322016641463101073880550463771174655651832418111719646949462291396009} to get \frac{24519928653854221733733552434404946937899825954937634816}{6170365191715177779482467945369860501784408913594010934644126825341528124785676079587681}.

$$\frac{24519928653854221733733552434404946937899825954937634816}{6170365191715177779482467945369860501784408913594010934644126825341528124785676079587681}$$

Factor

$$\frac{2 ^ {184}}{3 ^ {184}} = 3.9738213042522386 \times 10^{-33}$$