Let's solve this step-by-step.
### Step 1: Calculate the Cube of 7
To find [tex]\( 7^3 \)[/tex]:
[tex]\[ 7^3 = 7 \times 7 \times 7 = 343 \][/tex]
### Step 2: Calculate [tex]\( 2 \)[/tex] Raised to the Power of [tex]\( 3^2 \)[/tex]
First, we need to find [tex]\( 3^2 \)[/tex]:
[tex]\[ 3^2 = 3 \times 3 = 9 \][/tex]
Then, we use this result to find [tex]\( 2^9 \)[/tex]:
[tex]\[ 2^9 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 512 \][/tex]
### Step 3: Calculate the Square Root of [tex]\( 100 \times (98 - 17) \)[/tex]
#### Step 3.1: Calculate [tex]\( 98 - 17 \)[/tex]
[tex]\[ 98 - 17 = 81 \][/tex]
#### Step 3.2: Calculate [tex]\( 100 \times 81 \)[/tex]
[tex]\[ 100 \times 81 = 8100 \][/tex]
#### Step 3.3: Calculate the Square Root of 8100
[tex]\[ \sqrt{8100} = 90 \][/tex]
### Final Result
Combining all these results, we have:
1. [tex]\( 7^3 = 343 \)[/tex]
2. [tex]\( 2^{3^2} = 512 \)[/tex]
3. [tex]\( 98 - 17 = 81 \)[/tex]
4. [tex]\( 100 \times 81 = 8100 \)[/tex]
5. [tex]\( \sqrt{8100} = 90 \)[/tex]
Thus, the numerical results are [tex]\( 343 \)[/tex], [tex]\( 512 \)[/tex], [tex]\( 81 \)[/tex], [tex]\( 8100 \)[/tex], and [tex]\( 90 \)[/tex].
