Question 23

16y^8

When simplifying the expression \(((2y³)/(y^{0.25}))^4\), it can be rewritten as \((2^4 \cdot (y^3/y^{0.25})^4)\), leading to \(16y^{(3 - 0.25) \cdot 4}\), which equals \(16y^{8}\).

A) 8y^6

This option is incorrect because, when simplifying the exponent for \(y\), we find \(y^{(3 - 0.25) \cdot 4}\) results in \(y^{11}\), not \(y^6\). The coefficient of 8 also does not match the calculation.

B) 8y^11

This option is incorrect as the coefficient calculated is 16, not 8. While the exponent of \(y\) is correctly simplified to \(y^{11}\), the coefficient discrepancy disqualifies this choice.

C) 16y³

This option is incorrect since the exponent for \(y\) should be \(y^{11}\) rather than \(y^3\). The coefficient of 16 is accurate, but the exponent does not align with the correct simplification.

D) 16y^8

This option is correct because it accurately reflects the simplified form of the original expression. The calculation yields a coefficient of 16 and an exponent of \(y^8\), aligning perfectly with the simplification.

E) 16y^11

This option is incorrect as it claims a different exponent for \(y\). Although the coefficient of 16 is correct, the exponent should be \(y^8\), not \(y^{11}\).

Conclusion

The correct answer, \(16y^8\), accurately represents the simplification of the original expression. All other options either miscalculate the coefficient or the exponent of \(y\), confirming that D is the only choice that meets the criteria of the question.