question_answer

By what number should \[{{\left( -8 \right)}^{-3}}\]be multiplied so that the product may be equal to\[{{\left( -6 \right)}^{-3}}\] ?

Answer:

Let the number be x \[{{(-8)}^{-3}}\times x={{(-6)}^{-3}}\] \[{{\left( \frac{1}{-8} \right)}^{3}}\times x={{\left( \frac{1}{-6} \right)}^{3}}\]                                                                                                                           \[-\frac{1}{512}\times x=-\frac{1}{216}\]                                                                                                                                    \[x=\frac{512}{216}\] \[x=\frac{64}{27}\] \[x={{\left( \frac{4}{3} \right)}^{3}}\] \[x={{\left( \frac{3}{4} \right)}^{-3}}\]