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

$$\frac { 2 ^ { 4 } \times 2 ^ { 2 } \times 3 ^ { 2 } } { 3 ^ { 5 } \times 3 ^ { 4 } } ) ^ { 3 }$$

Evaluate

$$\frac{64}{2187}\approx 0.029263832$$

Solution Steps

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

$$\frac{2^{6}\times 3^{2}}{3^{5}\times 3^{4}}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

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

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

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

Calculate 2 to the power of 6 and get 64.

$$\frac{64}{3^{7}}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{64}{2187}$$

Factor

$$\frac{2 ^ {6}}{3 ^ {7}} = 0.029263831732967534$$