Question

Simplify the following:

a) ((w^-5)/(w^-9))^1/2
b) (m^6)^-2/3
c) (3x^-4y^5)/((2x^3y^-7))^-2

Answer 1

Problem A

`((w^(-5))/(w^(-9)))^{{(1)/(2)}` =
`((w^(9))/(w^(5)))^{{(1)/(2)}` =
`(w^(4))^{{(1)/(2)}` =
`\sqrt[2]{w^(4)}` =
`w^(2)`

Problem B

`(m^(6))^{-(2)/(3)}` =
`\frac{1}{(m^(6))^{(2)/(3)}}` =
`\frac{1}{\sqrt[3]{(m^(6))^(2)}}` =
`\frac{1}{\sqrt[3]{m^(12)}}` =
`(1)/(m^(4))`

Problem C

`((3x^(-4)y^(5))/(2x^(3)y^(-7)))^(-2)` =
`((3y^(12))/(2x^(7)))^(-2)` =
`((3y^(12))^(-2))/((2x^(7))^(-2))` =
`((2x^(7))^(2))/((3y^(12))^(2-))` =
`(4x^(14))/(9y^(24))`

Answer 2

a.
`((w^(-5))/(w^(-9) ))^{ (1)/(2) } \\ ( (w^(9) )/(w^(5) ))^{ (1)/(2) } \\ (w^(9-5))^{ (1)/(2) } \\ (w^(4))^{ (1)/(2) } \\ \sqrt{w^(4) } \\ w^(2)`
b.
`(m^(6))^{ (-2)/(3) } \\ ((1)/(m^(6) ))^{(2)/(3) } \\ \frac{ \sqrt[3]{1^(2) } }{ \sqrt[3]{m^(6) }^(2) } \\ \frac{ \sqrt[3]{1} }{m^(2*2) } \\ (1)/(m^(4) )`
Hope this helps!