Solve (3^2)^3/2*(8^1/3)^2

$$( 3 ^ { 2 } ) ^ { 3 / 2 } \times ( 8 ^ { 1 / 3 } ) ^ { 2 }$$

Evaluate

$$108$$

Solution Steps

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

$$3^{3}\times \left(8^{\frac{1}{3}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$3^{3}\times 8^{\frac{2}{3}}$$

Calculate 3 to the power of 3 and get 27.

$$27\times 8^{\frac{2}{3}}$$

Calculate 8 to the power of \frac{2}{3} and get 4.

$$27\times 4$$

Multiply 27 and 4 to get 108.

$$108$$

Factor

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