Final answer:
The correct equation that explains why 1/9³ equals 3¹ is that 1/9³ is equal to 9^(-1*3), which simplifies to 9^(-1), and thus equals 1/9.
Step-by-step explanation:
The equation that justifies why 1/9³ = 3¹ is 1/9³ = 9^(-1/3*3) = 9^(-1) = 1/9. This can be explained by understanding exponent rules and negative exponents. When raising a number to a negative exponent, you are taking the reciprocal of that number raised to the positive exponent. Therefore, in the case of 1/9³, we are dealing with (9^-1)³. According to the rules of exponents, we can multiply the exponents together, giving us 9^(-1*3) or 9^-3. Finally, raising nine to the negative third power is equivalent to the reciprocal of nine cubed, which results in 1/9.