Solve 2^3*3^2*5*6/8*{9^frac{3{2}*10}}

$$\frac{ { 2 }^{ 3 } \times { 3 }^{ 2 } \times 5 \times 6 }{ 8 \times { 9 }^{ \frac{ 3 }{ 2 } \times 10 } }$$

Evaluate

$$\frac{10}{7625597484987}\approx 1.311372652 \cdot 10^{-12}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{3\times 5\times 2^{3}\times 3^{2}}{4\times 9^{\frac{3}{2}\times 10}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{3^{3}\times 5\times 2^{3}}{4\times 9^{\frac{3}{2}\times 10}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27\times 5\times 2^{3}}{4\times 9^{\frac{3}{2}\times 10}}$$

Multiply 27 and 5 to get 135.

$$\frac{135\times 2^{3}}{4\times 9^{\frac{3}{2}\times 10}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{135\times 8}{4\times 9^{\frac{3}{2}\times 10}}$$

Multiply 135 and 8 to get 1080.

$$\frac{1080}{4\times 9^{\frac{3}{2}\times 10}}$$

Multiply \frac{3}{2} and 10 to get 15.

$$\frac{1080}{4\times 9^{15}}$$

Calculate 9 to the power of 15 and get 205891132094649.

$$\frac{1080}{4\times 205891132094649}$$

Multiply 4 and 205891132094649 to get 823564528378596.

$$\frac{1080}{823564528378596}$$

Reduce the fraction \frac{1080}{823564528378596} to lowest terms by extracting and canceling out 108.

$$\frac{10}{7625597484987}$$

Factor

$$\frac{2 \cdot 5}{3 ^ {27}} = 1.3113726523970926 \times 10^{-12}$$