Here is the definition of a negative exponent.
For any non-zero value of a,
[tex] a^{-n} = \dfrac{1}{a^n} [/tex]
Look at your problem and follow the definition.
[tex] 4^{-3} = \dfrac{1}{4^3} [/tex]
Since 4^3 = 4 * 4 * 4 = 64, we can now write:
[tex] 4^{-3} = \dfrac{1}{4^3} = \dfrac{1}{4 \times 4 \times 4} = \dfrac{1}{64} [/tex]
