The given expression is simplified using algebric operation. The simplified form of [tex]\left[\dfrac{20x^5y^2}{5x^-^3y^7}\right]^{-3}[/tex] is given by the expression: [tex]\left[\dfrac{y^{15}}{64\times x^{24}}\right][/tex] .
Given :
Expression - [tex]\left[\dfrac{20x^5y^2}{5x^-^3y^7}\right]^{-3},\;x\neq 0,\;y\neq 0[/tex]
The given expression can be evaluated by using following steps:
Step 1 - Multiply numerator and denominator by [tex]x^{3}[/tex].
[tex]\left[\dfrac{20x^5y^2}{5x^-^3y^7}\right]^{-3} = \left[\dfrac{20x^8y^2}{5y^7}\right]^{-3}[/tex]
Step 2 - Multiply numerator and denominator by [tex]y^{-7}[/tex].
[tex]\left[\dfrac{20x^5y^2}{5x^-^3y^7}\right]^{-3} = \left[\dfrac{20x^8y^{-5}}{5}\right]^{-3}[/tex]
Step 3 - Further simplify the above expression.
[tex]\left[\dfrac{20x^5y^2}{5x^-^3y^7}\right]^{-3} = \left[{4^{-3}x^{-24}y^{15}}\right][/tex]
Step 4 - Rearrange the above expression.
[tex]\left[\dfrac{20x^5y^2}{5x^-^3y^7}\right]^{-3} = \left[\dfrac{y^{15}}{64\times x^{24}}\right][/tex]
The simplified form of [tex]\left[\dfrac{20x^5y^2}{5x^-^3y^7}\right]^{-3}[/tex] is given by the expression: [tex]\left[\dfrac{y^{15}}{64\times x^{24}}\right][/tex] .
For more information, refer the link given below: https://brainly.com/question/13911928
