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

$$\frac { 6 ^ { 9 } \cdot 6 ^ { 2 } } { ( 6 ^ { 2 } \cdot 6 ^ { 3 } ) ^ { 3 } }$$

Evaluate

$$\frac{1}{1296}\approx 0.000771605$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 2 to get 11.

$$\frac{6^{11}}{\left(6^{2}\times 6^{3}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{6^{11}}{\left(6^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{6^{11}}{6^{15}}$$

Rewrite 6^{15} as 6^{11}\times 6^{4}. Cancel out 6^{11} in both numerator and denominator.

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

Calculate 6 to the power of 4 and get 1296.

$$\frac{1}{1296}$$

Factor

$$\frac{1}{2 ^ {4} \cdot 3 ^ {4}} = 0.0007716049382716049$$