False, because according to the Negative Exponent Rule, the equation should be 10^-1/3 = -1/3√10.
To determine whether the equation 10^(-1/3) = -3√10 is true or false, we can use the properties of exponents. The Negative Exponent Rule states that when a number is raised to a negative exponent, it can be rewritten as the reciprocal of the number raised to the positive exponent. In this case, 10^(-1/3) can be rewritten as 1/(10^(1/3)).
To simplify this expression further, we need to evaluate the cube root of 10^(1/3). The cube root of a number can be written as the number raised to the exponent of 1/3.
So, the cube root of 10^(1/3) is (10^(1/3))^(1/3), which simplifies to 10^(1/9).
Therefore, the equation becomes 1/(10^(1/3)) = -3√10.
Comparing this with the given equation, we can see that the expression on the left-hand side is not equal to the expression on the right-hand side. Hence, the equation 10^(-1/3) = -3√10 is false.
The appropriate justification is false, because according to the Negative Exponent Rule, the equation should be 10^(-1/3) = -1/3√10.