Final answer:
None of the given expressions A) (2x)⁴, B) (4x)², C) (8x)², or D) (x)ⁱ⁶ are equivalent to 16x⁸. This is because none of the provided expressions, when expanded, will result in the product of 16 and x raised to the 8th power.
Step-by-step explanation:
The expressions that are equivalent to 16x⁸ follow the rule of exponents, which states that when we raise a base to an exponent, we multiply the exponent by the power that the base is raised to.
Looking at the options:
- (2x)⁴ = 2⁴ * x⁴ = 16x⁴; this is not equivalent to 16x⁸ because 2⁴ gives 16 but x is raised to the 4th power, not the 8th.
- (4x)² = 4² * x² = 16x²; this is not equivalent to 16x⁸ for similar reasons--x is raised to the 2nd power instead of the 8th.
- (8x)² = 8² * x² = 64x²; this is also not equivalent to 16x⁸ because while x is squared, 8 squared is 64, not 16.
- (x)ⁱ⁶ = xⁱ⁶; this only has the variable x raised to the 16th power, without the coefficient of 16, so it is not equivalent to 16x⁸.
Therefore, none of the given options are equivalent to 16x⁸.