Solve 3*(9^2)^frac{1{4}}*(81^3)^frac{5{6}}

$$3 \times ( 9 ^ { 2 } ) ^ { \frac { 1 } { 4 } } \times ( 81 ^ { 3 } ) ^ { \frac { 5 } { 6 } }$$

Evaluate

$$531441$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{1}{4} to get \frac{1}{2}.

$$3\times 9^{\frac{1}{2}}\times \left(81^{3}\right)^{\frac{5}{6}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and \frac{5}{6} to get \frac{5}{2}.

$$3\times 9^{\frac{1}{2}}\times 81^{\frac{5}{2}}$$

Calculate 9 to the power of \frac{1}{2} and get 3.

$$3\times 3\times 81^{\frac{5}{2}}$$

Multiply 3 and 3 to get 9.

$$9\times 81^{\frac{5}{2}}$$

Calculate 81 to the power of \frac{5}{2} and get 59049.

$$9\times 59049$$

Multiply 9 and 59049 to get 531441.

$$531441$$

Factor

$$3^{12}$$