Solve (4,5)^-2*2^3/(frac{4{2})^3*3^5}

$$\frac { ( 4,5 ) ^ { - 2 } \cdot 2 ^ { 3 } } { ( \frac { 4 } { 2 } ) ^ { 3 } \cdot 3 ^ { 5 } }$$

Evaluate

$$\frac{4}{19683}\approx 0,000203221$$

Solution Steps

Calculate 4,5 to the power of -2 and get \frac{4}{81}.

$$\frac{\frac{4}{81}\times 2^{3}}{\left(\frac{4}{2}\right)^{3}\times 3^{5}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{4}{81}\times 8}{\left(\frac{4}{2}\right)^{3}\times 3^{5}}$$

Multiply \frac{4}{81} and 8 to get \frac{32}{81}.

$$\frac{\frac{32}{81}}{\left(\frac{4}{2}\right)^{3}\times 3^{5}}$$

Divide 4 by 2 to get 2.

$$\frac{\frac{32}{81}}{2^{3}\times 3^{5}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{32}{81}}{8\times 3^{5}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{\frac{32}{81}}{8\times 243}$$

Multiply 8 and 243 to get 1944.

$$\frac{\frac{32}{81}}{1944}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {9}} = 0.00020322105370116343$$