The expression \( \left(5^{\frac{7}{3}}\right)\left(5^{\frac{8}{3}}\right) \) can be written as \( 5^{k} \) where \( k \) is a constant. The value of \( k \) is

To simplify the expression \( \left(5^{\frac{7}{3}}\right)\left(5^{\frac{8}{3}}\right) \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \). Applying this, we have: \[ 5^{\frac{7}{3}} \cdot 5^{\frac{8}{3}} = 5^{\frac{7}{3} + \frac{8}{3}}. \] Now, we add the exponents: \[ \frac{7}{3} + \frac{8}{3} = \frac{7 + 8}{3} = \frac{15}{3} = 5. \] Thus, the expression simplifies to: \[ 5^{5}. \] Therefore, the value of \( k \) is \( \boxed{5} \).