Determine if each pair of expressions is equivalent. Explain your reasoning. 1 / 3^ 2 and 3 - ^2 1 / 4^ - 3 and 4 ^ - 3

1 / 3^ 2 and 3^2 are equivalent

1 / 4^ - 3 and 4^ - 3 are not equivalent.

Step-by-step explanation:

According to one of the law of indices, given two numbers a and b

a^-b = 1/a^b

When a number is raised to a negative power, the equivalent form of the expression becomes a fraction when the negative power is removed.

Given this pair of expressions

1 / 3^ 2 and 3 - ^2

Both expression are equal by applying the law of indices above.

3^-2 = 1/3^2 (note that 3 serves as 'a' while 2 serves as 'b)

For the pair of expressions

1 / 4^ - 3 and 4 ^ - 3

Both expressions are not equal, becomes converting 4 ^ - 3 to a fraction suppose to neutralize the negative sign to give 1/4^3 instead of 1 / 4^ - 3.