Sure, let's work through the problem step-by-step.
### Step 1: Calculate [tex]\( a \)[/tex]
We need to multiply 0.5 by itself four times.
[tex]\[
a = 0.5 \times 0.5 \times 0.5 \times 0.5 = 0.0625
\][/tex]
### Step 2: Calculate [tex]\( B \)[/tex]
We need to multiply -6 by itself three times.
[tex]\[
B = (-6) \times (-6) \times (-6) = -216
\][/tex]
Note: Multiplying three negative factors yields a negative result.
### Step 3: Calculate [tex]\( c \)[/tex]
We need to multiply 7 by itself four times, multiply the result by 9, and then multiply the final result by [tex]\( a \)[/tex].
[tex]\[
c = 7 \times 7 \times 7 \times 7 \times 9 \times a = 1350.5625
\][/tex]
### Step 4: Calculate [tex]\( d \)[/tex]
We need to calculate the negative of 5 raised to the power of three.
[tex]\[
d = -1 \times (5 \times 5 \times 5) = -125
\][/tex]
Putting it all together, we have:
[tex]\[
a = 0.0625, \quad B = -216, \quad c = 1350.5625, \quad d = -125
\][/tex]
This gives us the final results:
[tex]\[
(a, B, c, d) = (0.0625, -216, 1350.5625, -125)
\][/tex]
