Solve frac{(2^{2})^{2}+(3^{3})^{2}}{(3^2)^3*(2^3)^4}

$$\frac { ( 2 ^ { 2 } ) ^ { 2 } + ( 3 ^ { 3 } ) ^ { 2 } } { ( 3 ^ { 2 } ) ^ { 3 } * ( 2 ^ { 3 } ) ^ { 4 } }$$

Evaluate

$$\frac{745}{2985984}\approx 0.000249499$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

$$\frac{2^{4}+3^{6}}{\left(3^{2}\right)^{3}\times \left(2^{3}\right)^{4}}$$

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

$$\frac{2^{4}+3^{6}}{3^{6}\times \left(2^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{2^{4}+3^{6}}{3^{6}\times 2^{12}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16+3^{6}}{3^{6}\times 2^{12}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{16+729}{3^{6}\times 2^{12}}$$

Add 16 and 729 to get 745.

$$\frac{745}{3^{6}\times 2^{12}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{745}{729\times 2^{12}}$$

Calculate 2 to the power of 12 and get 4096.

$$\frac{745}{729\times 4096}$$

Multiply 729 and 4096 to get 2985984.

$$\frac{745}{2985984}$$

Factor

$$\frac{5 \cdot 149}{2 ^ {12} \cdot 3 ^ {6}} = 0.00024949899262688614$$