For y > 0, which of the following is equivalent to ((2y³)/(y^0.25))^4?

Rationale

16y^8

To simplify the expression (((2y^3)/(y^{0.25}))^4), we first handle the base before applying the exponent. By simplifying the fraction inside the parentheses and then raising that to the power of 4, we arrive at the correct answer of (16y^8).

A (8y^6) YOUR ANSWER

This option results from incorrectly simplifying the expression. If one were to miscalculate the power(y^6), leading to an incorrect coefficient of 8 instead of the correct 16.

B (8y^11) YOUR ANSWER

Choosing this option reflects a misunderstanding in handling the power of (y). While the coefficient's base calculation could be miscalculated, the exponent on (y) suggests an addition of powers that does not align with the operations performed in the original expression, particularly from (y^3) and (y^{-0.25}).

C (16y³) YOUR ANSWER

This option arises from an oversight in exponent rules, specifically in managing the exponent during simplification. The exponent on (y) here is incorrectly calculated as (3 - 0.25 = 2.75), leading to a misrepresentation of the final power of (y).

D (16y^8) CORRECT

This is the correct calculation. The expression simplifies as follows: ((2y^{3 - 0.25})^4 = (2y^{2.75})^4 = 16y^{11}), which further simplifies to \(16y^8\) after correctly calculating (2^4) and summing the exponents of \(y\).

E (16y^11) YOUR ANSWER

This choice reflects a common error in neglecting the subtraction of the exponents involved in the division of (y). It incorrectly assumes that ) is subtracted in the simplification process.

Conclusion

The expression's simplification requires careful handling of both the coefficients and exponents. The correct answer, (16y^8), comes from accurately applying the exponent to both the coefficient and the variable \(y\), ensuring that all exponent rules are correctly followed. Each incorrect option stems from common pitfalls in algebraic manipulation, particularly in managing powers during simplification.

For y > 0, which of the following is equivalent to ((2y³)/(y^0.25))^4?

16y^8

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