Solve 9{left(1/2right)}^-218^5-left(-2^-2right)^-2{left(1/3right)}^-5{left(3^-3right)}^-2{left(1/6right)}^69

$$9 { \left( \frac{ 1 }{ 2 } \right) }^{ -2 } { 18 }^{ 5 } - { \left(- { 2 }^{ -2 } \right) }^{ -2 } { \left( \frac{ 1 }{ 3 } \right) }^{ -5 } { \left( { 3 }^{ -3 } \right) }^{ -2 } { \left( \frac{ 1 }{ 6 } \right) }^{ 69 }$$

Evaluate

$$\frac{11820817658190724978634830639161821526685317292206587903}{173773077264672915517592008084531924855683022848}\approx 68024448$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and -2 to get 6.

$$9\times \left(\frac{1}{2}\right)^{-2}\times 18^{5}-\left(-2^{-2}\right)^{-2}\times \left(\frac{1}{3}\right)^{-5}\times 3^{6}\times \left(\frac{1}{6}\right)^{69}$$

Calculate \frac{1}{2} to the power of -2 and get 4.

$$9\times 4\times 18^{5}-\left(-2^{-2}\right)^{-2}\times \left(\frac{1}{3}\right)^{-5}\times 3^{6}\times \left(\frac{1}{6}\right)^{69}$$

Multiply 9 and 4 to get 36.

$$36\times 18^{5}-\left(-2^{-2}\right)^{-2}\times \left(\frac{1}{3}\right)^{-5}\times 3^{6}\times \left(\frac{1}{6}\right)^{69}$$

Calculate 18 to the power of 5 and get 1889568.

$$36\times 1889568-\left(-2^{-2}\right)^{-2}\times \left(\frac{1}{3}\right)^{-5}\times 3^{6}\times \left(\frac{1}{6}\right)^{69}$$

Multiply 36 and 1889568 to get 68024448.

$$68024448-\left(-2^{-2}\right)^{-2}\times \left(\frac{1}{3}\right)^{-5}\times 3^{6}\times \left(\frac{1}{6}\right)^{69}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$68024448-\left(-\frac{1}{4}\right)^{-2}\times \left(\frac{1}{3}\right)^{-5}\times 3^{6}\times \left(\frac{1}{6}\right)^{69}$$

Calculate -\frac{1}{4} to the power of -2 and get 16.

$$68024448-16\times \left(\frac{1}{3}\right)^{-5}\times 3^{6}\times \left(\frac{1}{6}\right)^{69}$$

Calculate \frac{1}{3} to the power of -5 and get 243.

$$68024448-16\times 243\times 3^{6}\times \left(\frac{1}{6}\right)^{69}$$

Multiply 16 and 243 to get 3888.

$$68024448-3888\times 3^{6}\times \left(\frac{1}{6}\right)^{69}$$

Calculate 3 to the power of 6 and get 729.

$$68024448-3888\times 729\times \left(\frac{1}{6}\right)^{69}$$

Multiply 3888 and 729 to get 2834352.

$$68024448-2834352\times \left(\frac{1}{6}\right)^{69}$$

Calculate \frac{1}{6} to the power of 69 and get \frac{1}{492534069091280207443117943298409230278554887175274496}.

$$68024448-2834352\times \frac{1}{492534069091280207443117943298409230278554887175274496}$$

Multiply 2834352 and \frac{1}{492534069091280207443117943298409230278554887175274496} to get \frac{1}{173773077264672915517592008084531924855683022848}.

$$68024448-\frac{1}{173773077264672915517592008084531924855683022848}$$

Subtract \frac{1}{173773077264672915517592008084531924855683022848} from 68024448 to get \frac{11820817658190724978634830639161821526685317292206587903}{173773077264672915517592008084531924855683022848}.

$$\frac{11820817658190724978634830639161821526685317292206587903}{173773077264672915517592008084531924855683022848}$$