Question

(8/27)^-2/3 can be simplified to 9/4.... true or false

Answer 1

remember
`x^(-m)=(1)/(x^m)`
and

`((a)/(b))^c=(a^c)/(b^c)`
and

`x^(m)/(n)=\sqrt[n]{x^m}`
and

`(x^m)^n=x^(mn)`

so, combining all of those

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

`((1)/(8^(2)/(3)))/((1)/(27^(2)/(3)))=(27^(2)/(3))/(8(2)/(3))`=

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

`\frac{\sqrt[3]{3^6}}{\sqrt[3]{2^6}}=(3^ (6)/(3))/(2^ (6)/(3))`=

`(3^2)/(2^2)=(9)/(4)`

true

Answer 2

`\left( \cfrac{8}{27}\right)^{ -(2)/(3) } =\left( \cfrac{27}{8}\right)^{ (2)/(3) } = \sqrt[3]{\left( \cfrac{27}{8}\right)^(2 ) } =\sqrt[3]{ \cfrac{729}{64} } =\sqrt[3]{ \cfrac{9^3}{4^3} } = \cfrac{9}{4}`

True.