Question

6. Evaluate:
(ii) ³√-125
(iii) ⁴√256
(v)(32)^-3/5
(vi)(1/81)^3/4
(vii)³√(8/27)^2

Answer 1

Dear student
$$\begin{gathered} 2)\sqrt[3]{-125}=\sqrt[3]{\left(-5\right)\times \left(-5\right)\times \left(-5\right)}=-5 \\ 3)\sqrt[4]{256}=\sqrt[4]{4\times 4\times 4\times 4}=4 \\ 5){\left(32\right)}^{\frac{-3}{5}} \\ ={\left(2^5\right)}^{\frac{-3}{5}} \\ =2^{-3}\left[As{\left(a^m\right)}^n=a^{mn}\right] \\ =\frac{1}{2^3}\left[As{a}^{-m}=\frac{1}{a^m}\right] \\ =\frac{1}{8} \\ 6){\left(\frac{1}{81}\right)}^{\frac{3}{4}} \\ ={\left[{\left(\frac{1}{3}\right)}^4\right]}^{\frac{3}{4}} \\ ={\left(\frac{1}{3}\right)}^3 \\ =\frac{1}{27} \\ 7)\sqrt[3]{{\left(\frac{8}{27}\right)}^2} \\ ={\left(\frac{8}{27}\right)}^{\frac{2}{3}} \\ ={\left[{\left(\frac{2}{3}\right)}^3\right]}^{\frac{2}{3}} \\ ={\left(\frac{2}{3}\right)}^2 \\ =\frac{4}{9} \end{gathered}$$
Regards