Question The expression sqrt [3](5^5)cdot sqrt [3](5) is equivalent to Answer 25^2 x 5^2 25^(5)/(9) 5^(5)/(9)

To simplify the expression $\sqrt [3]{5^{5}}\cdot \sqrt [3]{5}$, we can use the property of exponents that states $\sqrt [n]{a^m} = a^{\frac{m}{n}}$. Applying this property, we have:<br /><br />$\sqrt [3]{5^{5}} = 5^{\frac{5}{3}}$<br /><br />$\sqrt [3]{5} = 5^{\frac{1}{3}}$<br /><br />Now, we can multiply these two expressions together:<br /><br />$5^{\frac{5}{3}} \cdot 5^{\frac{1}{3}} = 5^{\frac{5}{3} + \frac{1}{3}} = 5^{\frac{6}{3}} = 5^2$<br /><br />Therefore, the expression $\sqrt [3]{5^{5}}\cdot \sqrt [3]{5}$ is equivalent to $5^2$.