Question

Which choices are equivalent to the expression below? 3⁻²

a. -6
b. 1/9
c. 3²
d. 1/3²
e. 1
f. 2⁻³

Answer 1

The choices equivalent to the expression 3⁻² are 1/9 and 1/3², which are choices b and d respectively.

Step-by-step explanation:

To determine which choices are equivalent to the expression 3⁻², we must understand the negative exponent rule. According to this rule, the expression a⁻ⁿ is equivalent to 1/aⁿ for any non-zero 'a' and positive 'n'. Therefore, 3⁻² equals 1/3², which simplifies to 1/9.

1. Choice a. -6 is not equivalent because it is a negative integer, not a fraction.
2. Choice b. 1/9 is equivalent because it is the simplified form of 3⁻².
3. Choice c. 3² is not equivalent because it represents 9, not 1/9.
4. Choice d. 1/3² is equivalent because it represents the expression for 3⁻².
5. Choice e. 1 is not equivalent because it does not represent the expression for 3⁻².
6. Choice f. 2⁻³ is not equivalent because it represents 1/8, not 1/9.

The exponent -² means that we have a reciprocal of a square. In other words, it is equivalent to taking the square of the reciprocal value.

So, 3⁻²a is equivalent to (1/3²)a which simplifies to (1/9)a.

Therefore, the equivalent choice to the expression 3⁻²a is c. 3².

The correct answers are b and d.