Answer:
[tex]8^{\frac{x}{3} }[/tex] is the correct option.
Step-by-step explanation:
Here is the correct question: Which is equivalent to ∛8^x?
- [tex]\sqrt[x]{8^{3} }[/tex]
- [tex]8^{\frac{3}{x} }[/tex]
- [tex]8^{\frac{x}{3} }[/tex]
- [tex]8^{3x}[/tex]
As per rule; while writing exponent into fraction form, Power is considered as numerator and Root as denominator, however base remain same.
∴ For writing exponent to fraction: [tex]\sqrt[root]{base^{Power} } = base^{\frac{Power}{root} }[/tex]
Now, writing given exponent to fraction.
[tex]\sqrt[3]{8^{x} } = 8^{\frac{x}{3}}[/tex]
Hence, [tex]8^{\frac{x}{3} }[/tex] is the correct option.
