Answer:
Step-by-step explanation:
b). [tex](\frac{-7}{11})^{-8}\times [(\frac{-7}{11})^{-7}\div (\frac{-7}{11})^{-8}]^4[/tex]
= [tex](\frac{-7}{11})^{-8}\times [(\frac{-7}{11})^{-7}\times (\frac{-7}{11})^{8}]^4[/tex] [Since, [tex]\frac{1}{a^{-1}}=a[/tex]]
= [tex](\frac{-7}{11})^{-8}\times [(\frac{-7}{11})^{8-7}]^4[/tex]
= [tex](\frac{-7}{11})^{-8+4}[/tex]
= [tex](\frac{-7}{11})^{-4}[/tex]
= [tex](-\frac{11}{7})^4[/tex]
= [tex]\frac{14641}{2401}[/tex]
c). [tex](5^{-1}-10^{-1})^{-1}+(3^{-1}-5^{-1})^{-1}[/tex]
= [tex](\frac{1}{5}-\frac{1}{10})^{-1}+(\frac{1}{3}-\frac{1}{5})^{-1}[/tex]
= [tex](\frac{2}{10}-\frac{1}{10})^{-1}+(\frac{5}{15}-\frac{3}{15})^{-1}[/tex]
= [tex](\frac{1}{10})^{-1}+(\frac{2}{15})^{-1}[/tex]
= 10 + [tex]\frac{15}{2}[/tex]
= 10 + 7.5
= 17.5
