Is the answer 4? will explain later, it's diff to type on the phone.

vrowland wrote:Help? I don't understand how to break this problem down.


(1/2 ) power raised to -2 * (1/4) power raised to -2 * (1/16) power raised to -1 =[/img][/u]

it should be 2^10

(1/2 ) power raised to -2=(2^(-1))^(-2)=2^2
similarly,
(1/4) power raised to -2=4^2=2^4
(1/16) power raised to -1=16=2^4
hence
(1/2 ) power raised to -2 * (1/4) power raised to -2 * (1/16) power raised to -1 =(2^2)x(2^4)x(2^4)=2^10

one property of exponents is

(a) with the power m * (a)with the power n= (a) with the power (m + n)

so, (-2) with the power (1/2) * (-2)with the power (1/4) * (-1)with the power (1/16)

in this problem we have 2 bases, those are -1 and 2 so separate out both the bases with the exponents.

on doing so you will get

(-1)^(1/2)*(2)^(1/2)*(-1)^(1/4)*(2)^(1/4)*(-1)^(1/16)
(-1)^((1/2)+(1/4)+(1/16))* (2)^((1/2)+(1/4))
-1(2^(3/4))

if (1/2)is the power of -2, (1/4)is the power of -2, (1/16) is the power of -1