Alright, let's break down this expression into manageable steps and solve it step by step.
The given expression is:
[tex]\[
\left\{ (-2)^5 \times 3^5 \right\}^2 \div \left( 12 \times 3^7 \right)
\][/tex]
### Step 1: Evaluate [tex]\((-2)^5\)[/tex]
First, we need to calculate [tex]\((-2)^5\)[/tex]:
[tex]\[
(-2)^5 = -32
\][/tex]
### Step 2: Evaluate [tex]\(3^5\)[/tex]
Next, we calculate [tex]\(3^5\)[/tex]:
[tex]\[
3^5 = 243
\][/tex]
### Step 3: Multiply the results from Step 1 and Step 2
Now, we multiply the results from the previous steps:
[tex]\[
(-32) \times 243 = -7776
\][/tex]
### Step 4: Square the result from Step 3
Next, we take the result from Step 3 and square it:
[tex]\[
(-7776)^2 = 60466176
\][/tex]
### Step 5: Calculate the denominator [tex]\(12 \times 3^7\)[/tex]
Let's work on the denominator now. First, calculate [tex]\(3^7\)[/tex]:
[tex]\[
3^7 = 2187
\][/tex]
Then, multiply this by 12:
[tex]\[
12 \times 2187 = 26244
\][/tex]
### Step 6: Divide the result from Step 4 by the result from Step 5
Finally, we divide the result from Step 4 by the result from Step 5:
[tex]\[
\frac{60466176}{26244} = 2304.0
\][/tex]
Therefore, the value of the given expression [tex]\(\left\{ (-2)^5 \times 3^5 \right\}^2 \div \left( 12 \times 3^7 \right)\)[/tex] is:
[tex]\[
2304.0
\][/tex]
