Question

What is equal to the expression (4^-5)^3

Answer 1

The answer is 1/1073741824 or about 9.313 * 10^-10

Answer 2

Assuming the question is about this expression:

`(4^(-5))^3`

Use the exponent property

`(a^b)^c = a^(bc)`

to rewrite the expression as

`(4^(-5))^3 = 4^(-5\cdot 3) = 4^(-15)`

Now, recall that negative exponent behave as positive ones, except you have to invert the number beforehand (flip numerator and denominator). So:

`4^(-15) = \left((1)/(4)\right)^(15) = (1)/(4^(15))`