Answer:
[tex]\frac{1}{108}[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^m}[/tex]
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^m}[/tex]
[tex]a^{\frac{1}{3} }[/tex] × [tex]b^{-\frac{3}{2} }[/tex] ← substitute a = 8 and b = 36
= [tex]8^{\frac{1}{3} }[/tex] × [tex]36^{-\frac{3}{2} }[/tex]
= [tex]\sqrt[3]{8}[/tex] × [tex]\frac{1}{36^{\frac{3}{2} } }[/tex]
= 2 × [tex]\frac{1}{(\sqrt{36})^3 }[/tex]
= 2 [tex]\frac{1}{6^3}[/tex]
= 2 × [tex]\frac{1}{216}[/tex]
= [tex]\frac{1}{108}[/tex]
