Question

Which option lists am expression that is not equivalent to 4^2/3

0.25^2/3
0.25^-2/3
^3 square root of 16
(^3 square root of 4)^2

Answer 1

remember that

`x^{(a)/(b)}=\sqrt[b]{x^a}`

also
`x^(-a)=(1)/(x^a)`

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

so

`4^{(2)/(3)}`

first one, that one is clearly not equal since 0.25≠4

2nd one, 0.25=1/4, so
`0.25^{(-2)/(3)}=((1)/(4))^{(-2)/(3)=`
`\frac{1}{((1)/(4))^{(2)/(3)}}=4^{(2)/(3)}`, which matches

3rd one,
`\sqrt[3]{16}=\sqrt[3]{4^2}=4^{(3)/(2)}`, which matches

4th one
`(\sqrt[3]{4})^2=(4^{(1)/(3)})^2=4^{(2)/(3)}` which matches

answer is
`0.25^{(2)/(3)}`