Final answer:
After following the order of operations, the expression 4(4 + (2⁶ * 2⁻³)) simplifies to 48. The exponents are evaluated first, followed by the multiplication, to finally arrive at the answer.
Step-by-step explanation:
To solve the expression, we'll follow the order of operations, which means we'll first handle the parentheses and exponents before doing multiplication. The expression given is 4(4 + (2⁶ * 2⁻³)).
Let's start by evaluating the exponent part: 2⁶ means 2 multiplied six times which is 64. For 2⁻³, we have 1 divided by 2 cubed, which translates to 1/8 or 0.125 when written as a decimal. This gives us 4(4 + (64 * 0.125)).
Now we need to perform the multiplication inside the parentheses: 64 * 0.125 is equal to 8. So our expression now looks like this: 4(4 + 8).
Next, we will add the numbers inside the parentheses: 4 + 8 equals 12. Now we have 4 * 12.
Finally, we multiply 4 by 12 to get the final answer, which is 48.
The correct choice is A) 48.