Question

what NO. must be subtracted from {(-5/2)^3}^-3 to get (-2/5)^5​

Answer 1

To find:

• What number must be subtracted from {(-5/2)³}⁻³ to get (-2/5)⁵.

Step-by-step explanation:

First we will assume that x must be subtracted from {(-5/2)³}⁻³ to get (-2/5)⁵, then we will multiply the power of the number from which the x is subtracted. Then, {(-5/2)³}⁻³ - x , this expression is equal to (-2/5)⁵. Thus, forming an adequate equation and doing the basic mathematical calculations, we can easily find out the value of x, which is the required number.

Let's find out...

According to the question,

• {(-5/2)³}⁻³ - x = (-2/5)⁵
• (-5/2)⁻⁹ - x = (-2/5)⁵
• (-5/2)⁻⁹ - x = (-2/5)⁵
• (-2/5)⁹ - x = (-2/5)⁵
• (-2/5)⁹ = (-2/5)⁵ + x
• x = - (2/5)⁹ + (2/5)⁵
• x = - 512/1953125 + 32/3125
• x = (- 512 + 20000)/1953125
• x = 19488/1953125
• x = (19488/5⁹)

Therefore, 19488/1953125 must be subtracted from {(-5/2)³}⁻³ to get (-2/5)⁵.

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Answer 2

$\bf{ \pmb{ \underline{ \underline {\quad{GIVEN :}{\quad}}}}}$

$\\ \circ \: \: \: \: \sf what \: number \: must \: be \: subtracted \: from \: \bigg \{ \bigg( { {\frac{ - 5}{2}} \bigg)^{3} } \bigg \}^{ - 3} \: to \: get \: \bigg( \frac{ - 2}{5} \bigg)^5$

$\purple{ \bold{ \underline{ \underline {\quad{Solution :}{\quad}}}}}$

So, let's consider the number to be subtracted be x.

According to the Question:

$\\ \tt \: \bigg \{ \bigg( { {\frac{ - 5}{2}} \bigg)^{3} } \bigg \}^{ - 3} \: - x = \bigg( \frac{ - 2}{5} \bigg)^5 \\ \\ \\ \tt \: ⇢\bigg( { {\frac{ - 5}{2}} \bigg)^{ - 9} } - x = \bigg( \frac{ - 2}{5} \bigg)^5 \\ \\ \\ ⇢ \tt \: \bigg( { {\frac{ - 2}{5}} \bigg)^{ 9} } - x = \bigg( \frac{ - 2}{5} \bigg)^5 \\ \\ \\ \tt \: ⇢ - x = \bigg( \frac{ - 2}{5} \bigg)^5 - \bigg( { {\frac{ - 2}{5}} \bigg)^{ 9} } \\ \\ \\ \tt \: ⇢ - x = \frac{ - 32}{3125} - \frac{ - 512}{1953125} \\ \\ \\ \: \: \: \tt \: ⇢ - x = \frac{ - 20000 - ( - 512)}{1953125} \\ \\ \\ \tt \: ⇢ - x = \frac{ - 20000 + 512}{1953125} \\ \\ \\ \tt \: ⇢ - x = \frac { - 19488}{1953125} \\ \\ \\ \tt \: ⇢ x = \frac { 19488}{1953125} \\ \\ \\ \tt \: ⇢ x = \frac{19488}{ {5}^{9} }$

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