Question

EL QUE ME AYUDE CON ESTO LE DOY CORONA ._.

TEMA : TEORIA DE EXPONENTES

- Al aplicar la ley de exponentes la expresión se reduce a:

Answer 1

S =
`(36)/(25)`

Explanation:

Given expression is,

S =
`\sqrt[3]{[((3)/(2))^(-2)+6^(-3)+((3)/(2))^(-3)-6^(-1)}]^(-2)`

S =
`\sqrt[3]{[((2)/(3))^(2)+((1)/(6))^(3)+((2)/(3))^(3)-((1)/(6))}]^(-2)`

=
`\sqrt[3]{[(4)/(9)+(1)/(216)+(8)/(27)-(1)/(6)}]^(-2)`

=
`\sqrt[3]{((96+1+64-36)/(216))^(-2)}`

=
`\sqrt[3]{((125)/(216))^(-2)}`

=
`\sqrt[3]{((216)/(125))^(2)}`

=
`\sqrt[3]{((216)/(125))* ((216)/(125))}`

=
`\sqrt[3]{((6* 6* 6)/(5* 5* 5))* ((6* 6* 6)/(5* 5* 5))}`

=
`\sqrt[3]{((6)/(5))^3* ((6)/(5))^3}`

=
`(6)/(5)* (6)/(5)`

=
`(36)/(25)`