Solve 27*3^4*3^2/9^3*2^5

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

Evaluate

$$\frac{27}{32}=0.84375$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{27\times 3^{6}}{9^{3}\times 2^{5}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{27\times 729}{9^{3}\times 2^{5}}$$

Multiply 27 and 729 to get 19683.

$$\frac{19683}{9^{3}\times 2^{5}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{19683}{729\times 2^{5}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{19683}{729\times 32}$$

Multiply 729 and 32 to get 23328.

$$\frac{19683}{23328}$$

Reduce the fraction \frac{19683}{23328} to lowest terms by extracting and canceling out 729.

$$\frac{27}{32}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {5}} = 0.84375$$