Answer
$a)$ $9$
$b)$ $\dfrac{1}{7}$
$c)$ $\dfrac{1}{36}$
Work Step by Step
$a)$ $3^{2/7}\cdot3^{12/7}$
Evaluate the product of powers and simplify:
$3^{2/7}\cdot3^{12/7}=3^{2/7+12/7}=3^{14/7}=3^{2}=9$
$b)$ $\dfrac{7^{2/3}}{7^{5/3}}$
Evaluate the division and simplify:
$\dfrac{7^{2/3}}{7^{5/3}}=7^{2/3-5/3}=7^{-3/3}=7^{-1}=\dfrac{1}{7}$
$c)$ $(\sqrt[5]{6})^{-10}$
Write this expression as a fraction to change the sign of the exponent:
$(\sqrt[5]{6})^{-10}=\dfrac{1}{(\sqrt[5]{6})^{10}}=...$
Rewrite the radical expression as a power with rational exponent and simplify:
$...=\dfrac{1}{(6^{1/5})^{10}}=\dfrac{1}{6^{10/5}}=\dfrac{1}{6^{2}}=\dfrac{1}{36}$
