Solve 3^2*4^6*3/3^9*3*2=

$$\frac { 3 ^ { 2 } \times 4 ^ { 6 } \times 3 } { 3 ^ { 9 } \times 3 \times 2 } =$$

Evaluate

$$\frac{2048}{2187}\approx 0.936442615$$

Solution Steps

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

$$\frac{3^{3}\times 4^{6}}{3^{9}\times 3\times 2}$$

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\frac{3^{3}\times 4^{6}}{3^{10}\times 2}$$

Cancel out 3^{3} in both numerator and denominator.

$$\frac{4^{6}}{2\times 3^{7}}$$

Calculate 4 to the power of 6 and get 4096.

$$\frac{4096}{2\times 3^{7}}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{4096}{2\times 2187}$$

Multiply 2 and 2187 to get 4374.

$$\frac{4096}{4374}$$

Reduce the fraction \frac{4096}{4374} to lowest terms by extracting and canceling out 2.

$$\frac{2048}{2187}$$

Factor

$$\frac{2 ^ {11}}{3 ^ {7}} = 0.9364426154549611$$