The answer is -i
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The square root of 1/9 is 1/3 because the square root of 1 is 1 and the square root of 9 is 3.
The fraction in an exponent takes the base to that radical power (1/2 is take the square root, 1/3 is take the third or "cube" root, 1/5 is take the fifth root, etc) and the numerator to that positive power (2 is squared, 3 is cubed, etc) For example: 4 to the 1/2 power is the square root of 4, which is two. 4 to the 3/2 power is the square root of four, 2, taken to the third power, which is 8. Sources: Background Knowledge
The square root of 3 times the negative square root of 3 can be calculated by multiplying the two square roots together. This results in -3, as the square root of 3 multiplied by the square root of 3 is the square root of 9, which simplifies to 3. Multiplying this by the negative sign gives us -3.
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