Rationalize the denominator and simplify. Assume that the variable represents a positive real number. \[ \sqrt{\frac{2}{w}} \]

Which expression is equivalent to \( 7^{\frac{2}{5}} \) ?

Example 1 The coed soccer team has four times as many boys on it as it has girls. We say the ratio of the number of number of girls on the team is \( 4: 1 \). We read this as four to one.

Which expression is equivalent to \( \sqrt{10^{3}} \) ? \( 10^{\frac{2}{3}}-10^{\frac{3}{2}} \) \( 10^{\frac{1}{3}}-10^{6} \)

Which expression is equivalent to \( \sqrt[4]{6^{2}} \) ? \( 66^{8} \) \( 6^{\frac{1}{2}} \)

Which expression is equivalent to \( \sqrt{5} \) ? \( 5^{\frac{1}{2}} 2^{5} \) \( 5^{\frac{1}{5}} \)