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Please help me with this!!

Please help me with this!!-example-1
User Lucas Dias
by
7.7k points

1 Answer

8 votes

Answer:

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

User Peter Lyons
by
9.0k points

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