Solve 2^3*3^4*2^5*3^8/{3^5*{2}^9}

$$\frac{ { 2 }^{ 3 } \times { 3 }^{ 4 } \times { 2 }^{ 5 } \times { 3 }^{ 8 } }{ { 3 }^{ 5 } \times { 2 }^{ 9 } }$$

Evaluate

$$\frac{2187}{2}=1093.5$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{2^{8}\times 3^{4}\times 3^{8}}{3^{5}\times 2^{9}}$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$\frac{2^{8}\times 3^{12}}{3^{5}\times 2^{9}}$$

Cancel out 2^{8}\times 3^{5} in both numerator and denominator.

$$\frac{3^{7}}{2}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{2187}{2}$$

Factor

$$\frac{3 ^ {7}}{2} = 1093\frac{1}{2} = 1093.5$$