Question

Simplify the expression (2⁸⋅5−5⋅19⁰)−2⋅5-²/2³, then raise the result to the power of 4⋅228.

a) 0
b) 1
c) 2
d) 3

Answer 1

To simplify the given expression, we follow the order of operations and perform the necessary calculations step-by-step. The final answer is approximately 1.

Step-by-step explanation:

To simplify the expression (2⁸⋅5−5⋅19⁰)−2⋅5-²/2³, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Step 1: Inside the parentheses, we simplify the exponents:

(2⁸⋅5−5⋅19⁰)−2⋅5-²/8 = (256⋅5−5⋅1)−2⋅(1/25).

Step 2: Next, we perform the multiplications:

(1280−5)−2⋅(1/25) = 1275−2⋅(1/25).

Step 3: Now we divide:

1275−2⋅(0.04) = 1275−0.08.

Step 4: Finally, we subtract:

1275−0.08 = 1274.92.

Now, we raise the result to the power of 4⋅228:

1274.92^(4⋅228) = 1274.92^912.

The final answer is approximately 1.