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:

$4^{-15} = \left(\frac{1}{4}\right)^{15} = \frac{1}{4^{15}}$