Exponent meaning

Question

What does the exponent mean in (-64)^1/2? And what does the exponent stand for in (35x^-1y^-2/over 7x⁴y³?

Answer 1

exponent of 1/2 means square root, which is the square root function sqrt

sqrt(-64) = sqrt(-1 * 64) = sqrt(-1) * sqrt(64) = 8i

negative exponent on top ---> move it to the bottom

negative exponent on bottom --> move it to top

you get 35/ (7 x^5 y^5) = 5/(xy)^5