Question

Someone help me please ASAP

Answer 1

`((8)/(27))^{(-2)/(3)}`

=
`((27)/(8))^{(2)/(3)`

=
`\sqrt[3]{((27)/(8))^(2)}`

=
`\sqrt[3]{((27*27)/(8*8))}`

=
`(3*3)/(2*2)`

=
`(9)/(4)`

Error: Student did not use the negative sign properly

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`(x^(-6)y^(6))(x^{(-1)/(6)}y^(5))`

=
`x^(-6)*x^{(-1)/(6)}*y^(6)*y^(5)`

=
`x^{-6-{(1)/(6)}}*y^(6+5)`

=
`x^{{(-37)/(6)}}y^(11)`

=
`\frac{y^(11)}{x^{(37)/(6)}}`

Error: Student multiplied the exponents instead of adding them

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`(\frac{2m^{(1)/(4)}}{n^(4)})^(-4)`

=
`(2^(-4)m^(-1))/(n^(-16))`

=
`\frac{n^(16)}{{2^(4)m^(1)}}`

=
`\frac{n^(16)}{{16m}}`

Error: Student did not distribute the exponent properly AND did not use the negative sign properly