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Question

By what number should $${\left( {\dfrac{{ 2}}{-5}} \right)^{ - 3}}$$ be divided so that the quotient may be $${\left( {\dfrac{{ - 4}}{{125}}} \right)^{ - 2}}$$


Solution

 $${\left( {\dfrac{{ 2}}{-5}} \right)^{ - 3}}$$ = $${\left( {\dfrac{{ -5}}{2}} \right)^{  3}}$$

$${\left( {\dfrac{{ - 4}}{{125}}} \right)^{ - 2}}$$ = $${\left( {\dfrac{{ 125}}{{-4}}} \right)^{  2}}$$

let the number  $$= x$$

$$x\times{\left( {\dfrac{{ 125}}{{-4}}} \right)^{  2}}$$ = $${\left( {\dfrac{{ -5}}{2}} \right)^{  3}}$$

$$x=$$$${\left( {\dfrac{{ -125}}{8}} \right)^{  }}$$$${\left( {\dfrac{{ 16}}{125\times125}} \right)^{  }}$$

$$x=\dfrac{-2}{125}$$

Mathematics

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