Solve frac{(2^{3}*2^{2})^{2}*(3^3)^4}{(6^2)^5}

$$\frac { ( 2 ^ { 3 } \cdot 2 ^ { 2 } ) ^ { 2 } \cdot ( 3 ^ { 3 } ) ^ { 4 } } { ( 6 ^ { 2 } ) ^ { 5 } }$$

Evaluate

$$9$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{2^{10}\times \left(3^{3}\right)^{4}}{\left(6^{2}\right)^{5}}$$

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

$$\frac{2^{10}\times 3^{12}}{\left(6^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{2^{10}\times 3^{12}}{6^{10}}$$

Calculate 2 to the power of 10 and get 1024.

$$\frac{1024\times 3^{12}}{6^{10}}$$

Calculate 3 to the power of 12 and get 531441.

$$\frac{1024\times 531441}{6^{10}}$$

Multiply 1024 and 531441 to get 544195584.

$$\frac{544195584}{6^{10}}$$

Calculate 6 to the power of 10 and get 60466176.

$$\frac{544195584}{60466176}$$

Divide 544195584 by 60466176 to get 9.

$$9$$

Factor

$$3^{2}$$