Please help me with this!!
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Answer:
A, B, D, F
Step-by-step explanation:
Given expression: [tex]8^{\frac23}[/tex]
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^2)^{\frac13}[/tex]
Apply exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]
[tex]\implies (8^2)^{\frac13}=\sqrt[3]{8^2}[/tex]
Therefore, option A
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
Apply exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]
[tex]\implies (8^{\frac13})^2=(\sqrt[3]{8})^2[/tex]
Therefore, option B
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
As [tex]8^{\frac13}=2[/tex]
[tex]\implies (8^{\frac13})^2=2^2[/tex]
Therefore, option D
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
As [tex]8^{\frac13}=2[/tex]
[tex]\implies (8^{\frac13})^2=2^2[/tex]
[tex]\implies 2^2=4[/tex]
Therefore, option F