Solve 6^5div(6^frac{2{3}})^9*6^4

$$6 ^ { 5 } \div ( 6 ^ { \frac { 2 } { 3 } } ) ^ { 9 } \times 6 ^ { 4 }$$

Evaluate

$$216$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and 9 to get 6.

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

Rewrite 6^{6} as 6\times 6^{5}. Cancel out 6^{5} in both numerator and denominator.

$$\frac{1}{6}\times 6^{4}$$

Calculate 6 to the power of 4 and get 1296.

$$\frac{1}{6}\times 1296$$

Multiply \frac{1}{6} and 1296 to get 216.

$$216$$

Factor

$$2^{3}\times 3^{3}$$