Answer
$a)$ $5$
$b)$ $3^{1/5}$
$c)$ $4$
Work Step by Step
$a)$ $5^{2/3}\cdot5^{1/3}$
Evaluate the product by adding the exponents:
$5^{2/3}\cdot5^{1/3}=5^{3/3}=5^{1}=5$
$b)$ $\dfrac{3^{3/5}}{3^{2/5}}$
Evaluate the division by substracting the exponents:
$\dfrac{3^{3/5}}{3^{2/5}}=3^{3/5-2/5}=3^{1/5}$
$c)$ $(\sqrt[3]{4})^{3}$
Since we have the cubic root of a number cubed, this expressions can be simplified by just removing both the root and the exponent:
$(\sqrt[3]{4})^{3}=4$
