Question

Which expression is equivalent to 16/x²

a.(16/2)²
b.(4/x²)²
c.(4/x)²
d.(2/x)²

Answer 1

The equivalent expression to 16/x² is Option c. (4/x)², as it simplifies directly to the original expression when squared.

Step-by-step explanation:

The question asks which expression is equivalent to 16/x². To find an equivalent expression, we need to identify a pattern or perform a mathematical operation that simplifies or restructures the original expression without changing its value. We start by analyzing the given options:

• Option a. ¼(16/2)² = (¼×16)² = 8² = 64, which is not equivalent to 16/x².
• Option b. (4/x²)² = 4² / x²² = 16/x´, which is also not equivalent to 16/x².
• Option c. (4/x)² = 4² / x² = 16/x², which is indeed equivalent to 16/x².
• Option d. (2/x)² = 2² / x² = 4/x², which is not equivalent to 16/x².

Thus, the expression that is equivalent to 16/x² is Option c. (4/x)².