Sure, let's simplify the expression step-by-step:
We start with the given expression:
[tex]\[ 7(3 - 1.8)^9 \][/tex]
First, simplify the expression inside the parentheses:
[tex]\[ 3 - 1.8 = 1.2 \][/tex]
Now, substitute this value back into the expression:
[tex]\[ 7(1.2)^9 \][/tex]
Next, calculate the value of [tex]\( 1.2^9 \)[/tex]. This computation yields:
[tex]\[ 1.2^9 \approx 5.159637 \][/tex]
Then, multiply this result by 7:
[tex]\[ 7 \times 5.159637 \approx 36.118462464 \][/tex]
Thus, the simplified value of the expression [tex]\( 7(3 - 1.8)^9 \)[/tex] is approximately [tex]\( 36.118462464 \)[/tex].
Now, let's compare this result to the given options:
- Option a: 4165.55
- Option b: 219.35
- Option c: 36.12
The value [tex]\( 36.118462464 \)[/tex] is very close to [tex]\( 36.12 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{36.12} \][/tex]
