Question

simplify the following expressions.
a) \\(\sqrt5{\dfrac{m^{16}}{m}}\\)
\\(m^3\\)
b) \\(\sqrt4{\dfrac{r^{10}}{r^2}}\\)

Explanation:

Step1: Simplify exponent inside root

$\sqrt[5]{\frac{m^{16}}{m}} = \sqrt[5]{m^{16-1}} = \sqrt[5]{m^{15}}$

Step2: Convert root to exponent form

$\sqrt[5]{m^{15}} = m^{\frac{15}{5}}$

Step3: Simplify the exponent

$m^{\frac{15}{5}} = m^3$

Step4: Simplify exponent inside root

$\sqrt[4]{\frac{r^{10}}{r^2}} = \sqrt[4]{r^{10-2}} = \sqrt[4]{r^8}$

Step5: Convert root to exponent form

$\sqrt[4]{r^8} = r^{\frac{8}{4}}$

Step6: Simplify the exponent

$r^{\frac{8}{4}} = r^2$

Answer:

a) $m^3$
b) $r^2$