Question

Find the value of the following expression:

(2^8 x 5^-5 x 19^0)^-2 x (5^-2/ 2^3)^4 x 2^28

I tried to do a couple steps to solve the question but I don't know if its right.

Step 1:(2^8 x 5^-5 x 19^0)^-2 x (5^-2/ 2^3)^4 x 2^28
Step 2: (2^-16 x 5^-10) x (5^-2/ 2^3)^4 x 2^28
Step 3: (2^-16 x 5^-10) x (5^-8/ 2^12) x 2^26

Answer 1

You lost a minus sign and made a typo. The steps should be

(2^-16 x 5^10) x (5^-2/ 2^3)^4 x 2^28
(2^-16 x 5^10) x (5^-8/ 2^12) x 2^28

Now just collect powers on each base factor.

2^(-16-12+28) x 5^(10-8)
= 5^2
= 25

Answer 2

You made a mistake on step 2. Should be:
Step 1:(2^8 x 5^-5 x 19^0)^-2 x (5^-2/ 2^3)^4 x 2^28
Step 2: (2^-16 x 5^10) x (5^-2/ 2^3)^4 x 2^28
Step 3: (2^-16 x 5^10) x (5^-8/ 2^12) x 2^28

Now expanding out:
Step 4: 2^-16 x 2^12 x 2^28 x 5^10 x 5^-8
Step 5: 2^24 x 5^2
Step 6: 25 x 2^24
Step 7: 25 x 16777216
Step 8: 419430400

Answer 3

Im confused. How did you guys end up with two different answers?