Question

By what number should [(-5\2)power3]power-3 be multiplied to get (-2\5)power5

Answer 1

Answer:

${ (\frac{5}{2} )}^{4}$

Step-by-step explanation:

Let the number be x

Therefore according to the question-

${[( { \frac{ - 5}{2})}^{3}]} ^{ - 3} \times x = { (\frac{ - 2}{5} )}^{5} \\ \\ = > {( \frac{ - 125}{8} )}^{ - 3} x = \frac{ - 32}{3125} \\ \\ = > { (\frac{ - 8}{125}) }^{3} x = \frac{ - 32}{3125} \\ \\ = > \frac{ - 512}{1953125} x = \frac{ - 32}{3125} \\ \\ = > x = \frac{ - 32}{3125} \times \frac{ - 1953125}{512} \\ \\ = > x = \frac{625}{16} \\ \\ = > x = {( \frac{5}{2}) }^{4}$