Certainly! Let's break down and solve the expression step by step:
[tex]\[
\left(9^2 + 1\right) - 2^4 \times \sqrt{16} + (12 + 3 \times 5) - 7
\][/tex]
### Step 1: Calculate [tex]\(9^2 + 1\)[/tex]
First, compute [tex]\(9^2\)[/tex]:
[tex]\[
9^2 = 81
\][/tex]
Now add 1 to the result:
[tex]\[
9^2 + 1 = 81 + 1 = 82
\][/tex]
### Step 2: Calculate [tex]\(2^4 \times \sqrt{16}\)[/tex]
First, compute [tex]\(2^4\)[/tex]:
[tex]\[
2^4 = 16
\][/tex]
Next, compute [tex]\(\sqrt{16}\)[/tex]:
[tex]\[
\sqrt{16} = 4
\][/tex]
Now multiply the two results together:
[tex]\[
2^4 \times \sqrt{16} = 16 \times 4 = 64
\][/tex]
### Step 3: Calculate [tex]\(12 + 3 \times 5\)[/tex]
First, compute [tex]\(3 \times 5\)[/tex]:
[tex]\[
3 \times 5 = 15
\][/tex]
Now add 15 to 12:
[tex]\[
12 + 3 \times 5 = 12 + 15 = 27
\][/tex]
### Step 4: Combine the calculated values
Now, substitute the calculated values back into the original expression:
[tex]\[
(82) - (64) + (27) - (7)
\][/tex]
Perform the subtraction and addition steps in order:
1. Subtract 64 from 82:
[tex]\[
82 - 64 = 18
\][/tex]
2. Add 27 to 18:
[tex]\[
18 + 27 = 45
\][/tex]
3. Finally, subtract 7 from 45:
[tex]\[
45 - 7 = 38
\][/tex]
### Conclusion
Thus, the value of the expression [tex]\(\left(9^2 + 1\right) - 2^4 \times \sqrt{16} + (12 + 3 \times 5) - 7\)[/tex] is:
[tex]\[
\boxed{38}
\][/tex]
