Answer:
[tex]\frac{1}{27}[/tex]
Step-by-step explanation:
Using the rules of exponents/ radicals
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]
Given
[tex]9^{-\frac{1}{2} }[/tex] × [tex]27^{-\frac{2}{3} }[/tex]
= [tex]\frac{1}{9^{\frac{1}{2} } }[/tex] × [tex]\frac{1}{27^{\frac{2}{3} } }[/tex]
= [tex]\frac{1}{\sqrt{9} }[/tex] × [tex]\frac{1}{\sqrt[3]{27^{2} } }[/tex]
= [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3^{2} }[/tex]
= [tex]\frac{1}{3}[/tex] ×[tex]\frac{1}{9}[/tex]
= [tex]\frac{1}{27}[/tex]
