Answer:
[tex] \displaystyle 1 \quad \cdot \quad \: \boxed{\frac{1}{2} } \\ 2 \quad \cdot \quad \: \boxed{\frac{62500}{729} }[/tex]
Step-by-step explanation:
a.
[tex] \displaystyle \large{ \sf{ \implies\bigg \{ \bigg \lgroup \frac{1}{5} \bigg \rgroup^{ - 1} - \bigg \lgroup \frac{1}{3} \bigg \rgroup ^{ - 1} \bigg \}^{ - 1} }}[/tex]
[tex] \displaystyle \large{ \sf{ \implies\bigg \{5 - 3 \bigg \}^{ - 1} }}[/tex]
[tex] \displaystyle \large{ \sf{ \implies\bigg \{2 \bigg \}^{ - 1} }}[/tex]
[tex] \displaystyle \large{ \sf{ \implies \frac{1}{2} }}[/tex]
b.
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{3}{5} { \bigg)}^{ - 8} \times \bigg( \frac{5}{6} { \bigg)}^{ - 2} }[/tex]
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{5}{3} { \bigg)}^{8} \times \bigg( \frac{6}{5} { \bigg)}^{ 2} }[/tex]
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{5}{3} { \bigg)}^{8} \times \bigg( \frac{2 \times 3}{5} { \bigg)}^{ 2} }[/tex]
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{ {5}^{8} }{ {3}^{8} } { \bigg)}\times \bigg( \frac{ {2}^{2} \times {3}^{2} }{ {5}^{2} } { \bigg)} }[/tex]
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{ {5}^{6} }{ {3}^{6} } { \bigg)}\times \bigg( \frac{ {2}^{2}}{1} { \bigg)} }[/tex]
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{ {5}^{6} \times {2}^{2} }{ {3}^{6} } { \bigg)} }[/tex]
[tex] \large \displaystyle \sf{ \implies \frac{ ({5}^{3} \times {2}^{1} {)}^{2} }{ ({3}^{2} {)}^{3} } { } }[/tex]
[tex] \large \displaystyle \sf{ \implies { \frac{62500}{729} } }[/tex]
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Answers & Comments
Answer:
[tex] \displaystyle 1 \quad \cdot \quad \: \boxed{\frac{1}{2} } \\ 2 \quad \cdot \quad \: \boxed{\frac{62500}{729} }[/tex]
Step-by-step explanation:
a.
[tex] \displaystyle \large{ \sf{ \implies\bigg \{ \bigg \lgroup \frac{1}{5} \bigg \rgroup^{ - 1} - \bigg \lgroup \frac{1}{3} \bigg \rgroup ^{ - 1} \bigg \}^{ - 1} }}[/tex]
[tex] \displaystyle \large{ \sf{ \implies\bigg \{5 - 3 \bigg \}^{ - 1} }}[/tex]
[tex] \displaystyle \large{ \sf{ \implies\bigg \{2 \bigg \}^{ - 1} }}[/tex]
[tex] \displaystyle \large{ \sf{ \implies \frac{1}{2} }}[/tex]
b.
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{3}{5} { \bigg)}^{ - 8} \times \bigg( \frac{5}{6} { \bigg)}^{ - 2} }[/tex]
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{5}{3} { \bigg)}^{8} \times \bigg( \frac{6}{5} { \bigg)}^{ 2} }[/tex]
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{5}{3} { \bigg)}^{8} \times \bigg( \frac{2 \times 3}{5} { \bigg)}^{ 2} }[/tex]
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{ {5}^{8} }{ {3}^{8} } { \bigg)}\times \bigg( \frac{ {2}^{2} \times {3}^{2} }{ {5}^{2} } { \bigg)} }[/tex]
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{ {5}^{6} }{ {3}^{6} } { \bigg)}\times \bigg( \frac{ {2}^{2}}{1} { \bigg)} }[/tex]
[tex] \large \displaystyle \sf{ \implies \bigg( \frac{ {5}^{6} \times {2}^{2} }{ {3}^{6} } { \bigg)} }[/tex]
[tex] \large \displaystyle \sf{ \implies \frac{ ({5}^{3} \times {2}^{1} {)}^{2} }{ ({3}^{2} {)}^{3} } { } }[/tex]
[tex] \large \displaystyle \sf{ \implies { \frac{62500}{729} } }[/tex]