Question

Which expressions are equivalent to (- 1/2x²y⁴)? Select all that apply.

a) 1/4x⁴y⁸
b) - 1/4x⁴y⁸
c) 1/2x⁴y⁸
d) -x⁴y⁸

Answer 1

None of the provided options are equivalent to the expression (- 1/2x²y⁴) since they either differ in coefficients, exponents, or both.

Step-by-step explanation:

The student is asking for equivalent expressions to the given expression (- 1/2x²y⁴).

To find equivalent expressions, we look for expressions that have the same value when the same values for variables are substituted in. In this case, none of the provided options (a) 1/4x⁴y⁸, b) - 1/4x⁴y⁸, c) 1/2x⁴y⁸, and d) -x⁴y⁸) are equivalent because they either have different coefficients, different exponents, or both.

For example, if we attempt to compare option (a) to the original expression, raising the power of both variables results in a different value. Moreover, the coefficient in option (a) is positive whereas the original expression has a negative coefficient. These details ensure the expressions are not equivalent. Similar evaluations can be made for the other options.