Question

Negative exponents: (2x)^-3 does it look like 8/x^3, 8x^3, x^3/8, or 1/8x^3?

Answer 1

\[(2x)^{-3}={1\over(2x)^{3}}={1\over8x^{3}}=(8x^{3})^{-1}={1\over8}\times {1\over x^{3}}=8^{-1}\times({x^{3}})^{-1} \]

How's that?

Answer 2

Positive exponent -powers (squares, etc)
Negative exponent-reciprocal (one over)
Fractional exponent - root (eg 1/2 is sqrt)