Question

Please help me with this!!

Answer 1

A, B, D, F

Explanation:

Given expression:
`8^(\frac23)`

Apply exponent rule
`a^(bc)=(a^b)^c`

`\implies 8^(\frac23)=(8^2)^(\frac13)`

Apply exponent rule
`a^{(1)/(n)}=\sqrt[n]{a}`

`\implies (8^2)^(\frac13)=\sqrt[3]{8^2}`

Therefore, option A

Apply exponent rule
`a^(bc)=(a^b)^c`

`\implies 8^(\frac23)=(8^(\frac13))^2`

Apply exponent rule
`a^{(1)/(n)}=\sqrt[n]{a}`

`\implies (8^(\frac13))^2=(\sqrt[3]{8})^2`

Therefore, option B

Apply exponent rule
`a^(bc)=(a^b)^c`

`\implies 8^(\frac23)=(8^(\frac13))^2`

As
`8^(\frac13)=2`

`\implies (8^(\frac13))^2=2^2`

Therefore, option D

Apply exponent rule
`a^(bc)=(a^b)^c`

`\implies 8^(\frac23)=(8^(\frac13))^2`

As
`8^(\frac13)=2`

`\implies (8^(\frac13))^2=2^2`

`\implies 2^2=4`

Therefore, option F