what does 4^-3 really mean?

4^-3

first do you know what 4^3 means

it is read as 4 to the power of 3 and it means 4*4*4 that is 3 times 4

Now 4^-3 is nothing but 1/4^3

it is

(1/4)*(1/4)*(1/4)

- represent inverse we just need to change base from denominator to numerator and vice versa and power becomes +.

like vise (1/4^-3) would be 4^3.

1/4^3

4‾³ = 1/4³ = 1/64

4^-3 means (1/4)^3 = 1/(4 x 4 x 4) = 1/64

4^-3 = (1/4)^3 = 1/64

The negative means the inverse

1/4^3

1/64

1/64

1 over 64