Question

1. write each expression in radical form, or write each radical in exponential form.

a. $3^{1/6}$
b. $sqrt4{15^3} =$
c. $(c^3)^{3/5}$
d. $sqrt3{6xy^2}$

Explanation:

Step1: Convert exponent to radical

$3^{1/6} = \sqrt[6]{3}$

Step2: Convert radical to exponent

$\sqrt[4]{15^3} = 15^{3/4}$

Step3: Simplify exponent first, then convert

First simplify the exponent: $(c^3)^{3/5} = c^{3 \times \frac{3}{5}} = c^{9/5}$, then convert to radical: $c^{9/5} = \sqrt[5]{c^9}$

Step4: Convert radical to exponent

$\sqrt[3]{6xy^2} = (6xy^2)^{1/3}$

Answer:

a. $\sqrt[6]{3}$
b. $15^{3/4}$
c. $\sqrt[5]{c^9}$ (or $c^{9/5}$ is also acceptable as an exponential form)
d. $(6xy^2)^{1/3}$