Question

Find the value of the following expression: (2^8 • 5^-5 • 19^0)^-2 • (5^-2 over 2^3)^4 • 2^28. Write your answer in simplified form. Show all of your steps.

Answer 1

Recognize that "( ) over 2^3" means ( ) • 2^-3. Use the rule of exponents
.. (a^b)^c = a^(b•c)

= 2^-16•5^10•19^-2 • 5^-8*2^-12 • 2^28

Now, you can use the rule of exponents
.. (a^b)*(a^c) = a^(b+c)

= 2^(-16 -12 +28) • 5^(10 -8) • 19^-2
= 5^2 • 19^-2
= 5^2 / 19^2
= 25/361