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

Question

asked Aug 3, 2019 164k views

2 Answers

Dannybucks · Answer 1 · 2019-08-07T11:04:13+0000

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:

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