Solve 21*2^frac{1{2}}*2^frac{1{3}}*2^frac{1{6}}?

$$21 \cdot 2 ^ { \frac { 1 } { 2 } } \cdot 2 ^ { \frac { 1 } { 3 } } \cdot 2 ^ { \frac { 1 } { 6 } } ?$$

Evaluate

$$42$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{1}{2} and \frac{1}{3} to get \frac{5}{6}.

$$21\times 2^{\frac{5}{6}}\times 2^{\frac{1}{6}}$$

To multiply powers of the same base, add their exponents. Add \frac{5}{6} and \frac{1}{6} to get 1.

$$21\times 2^{1}$$

Calculate 2 to the power of 1 and get 2.

$$21\times 2$$

Multiply 21 and 2 to get 42.

$$42$$

Factor

$$2\times 3\times 7$$