Answer:
(2xy)⁴/x²y⁵
(4x)²/y
(4x)²y¯¹
Explanation:
From the question given above, we obtained:
16x²/y
Thus, we can obtain the equivalent of the above expression as follow:
For Option 1:
(2x)⁴/x²y¯¹ = 2⁴x⁴/x²y¯¹
(2x)⁴/x²y¯¹ = 16x⁴/x²y¯¹
Recall:
1/A¯¹ = A
Therefore,
16x⁴/x²y¯¹ = 16x⁴y/x²
Recall:
Aᵐ ÷ Aⁿ = Aᵐ ¯ ⁿ
Therefore,
16x⁴y/x² = 16x⁴¯²y = 16x²y
(2x)⁴/x²y¯¹ = 16x²y
Thus, (2x)⁴/x²y¯¹ is not equivalent to 16x²/y
For Option 2:
(2xy)⁴/x²y⁵ = 2⁴x⁴y⁴/x²y⁵
(2xy)⁴/x²y⁵ = 16x⁴y⁴/x²y⁵
Recall:
Aᵐ ÷ Aⁿ = Aᵐ ¯ ⁿ
16x⁴¯² y⁴¯⁵ = 16x²y¯¹
Recall:
A¯¹ = 1/A
16x²y¯¹ = 16x²/y
(2xy)⁴/x²y⁵ = 16x²/y
Thus, (2xy)⁴/x²y⁵ is equivalent to 16x²/y
For Option 3:
(4x)²/y = 4²x²/y
(4x)²/y = 16x²/y
Thus, (4x)²/y is equivalent to 16x²/y
For Option 4:
(4x)²y¯¹ = 4²x²y¯¹
(4x)²y¯¹ = 16x²y¯¹
Recall:
A¯¹ = 1/A
16x²y¯¹ = 16x²/y
(4x)²y¯¹ = 16x²/y
Thus, (4x)²y¯¹ is equivalent to 16x²/y
For Option 5:
(4x/y)²
Recall:
(A/B)ⁿ = Aⁿ / Bⁿ
(4x/y)² = (4x)²/y²
(4x/y)² = 4²x²/y²
(4x/y)² = 16x²/y²
Thus, (4x/y)² is not equivalent to 16x²/y
SUMMARY:
(2x)⁴/x²y¯¹ is not equivalent to 16x²/y
(2xy)⁴/x²y⁵ is equivalent to 16x²/y
(4x)²/y is equivalent to 16x²/y
(4x)²y¯¹ is equivalent to 16x²/y
(4x/y)² is not equivalent to 16x²/y