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

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

Evaluate

$$104976$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{3^{5}\times 2^{4}\times 2^{6}\times 3\times 3^{8}}{\left(2^{3}\right)^{2}\times 3^{6}}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{3^{6}\times 2^{4}\times 2^{6}\times 3^{8}}{\left(2^{3}\right)^{2}\times 3^{6}}$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$\frac{3^{14}\times 2^{4}\times 2^{6}}{\left(2^{3}\right)^{2}\times 3^{6}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{3^{14}\times 2^{10}}{\left(2^{3}\right)^{2}\times 3^{6}}$$

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

$$\frac{3^{14}\times 2^{10}}{2^{6}\times 3^{6}}$$

Cancel out 2^{6}\times 3^{6} in both numerator and denominator.

$$2^{4}\times 3^{8}$$

Calculate 2 to the power of 4 and get 16.

$$16\times 3^{8}$$

Calculate 3 to the power of 8 and get 6561.

$$16\times 6561$$

Multiply 16 and 6561 to get 104976.

$$104976$$

Factor

$$2^{4}\times 3^{8}$$