Answer:
6.25
Step-by-step explanation:
Using the rules of exponents
[tex](\frac{a}{b}) ^{-\frac{m}{n} }[/tex] = [tex](\frac{b}{a}) ^{\frac{m}{n} }[/tex]
[tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a} )^m[/tex]
Given
[tex](\frac{8}{125}) ^{-\frac{2}{3} }[/tex]
= [tex](\frac{125}{8}) ^{\frac{2}{3} }[/tex]
= [tex](\sqrt[3]{125} )^2[/tex] × [tex]\frac{1}{(\sqrt[3]{8})^2 }[/tex]
= 5² × [tex]\frac{1}{2^2}[/tex]
= 25 × [tex]\frac{1}{4}[/tex]
= [tex]\frac{25}{4}[/tex]
= 6.25
