Certainly! Let's simplify the given expression step-by-step:
The given expression is:
[tex]\[
\left(3^2\right)\left[(4-2)^3-\left(2+1^0\right)\right]
\][/tex]
1. Simplify the first part inside the parentheses:
- Calculate [tex]\(3^2\)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
2. Simplify the second part inside the outer brackets:
- First, handle the expression [tex]\((4-2)\)[/tex]:
[tex]\[
4 - 2 = 2
\][/tex]
- Then, raise this result to the power of 3:
[tex]\[
2^3 = 8
\][/tex]
3. Simplify the expression inside the second set of parentheses:
- Evaluate the power inside the parentheses:
[tex]\[
1^0 = 1
\][/tex]
- Then, add it to 2:
[tex]\[
2 + 1 = 3
\][/tex]
4. Subtract the results obtained in steps 2 and 3:
- Subtract the value obtained in step 3 from the value in step 2:
[tex]\[
8 - 3 = 5
\][/tex]
5. Multiply the result from step 1 by the result from step 4:
- Multiply [tex]\(9\)[/tex] by [tex]\(5\)[/tex]:
[tex]\[
9 \times 5 = 45
\][/tex]
Thus, the simplified expression is:
[tex]\[
45
\][/tex]
In summary:
[tex]\[
\left(3^2\right)\left[(4-2)^3-\left(2+1^0\right)\right] = \left(9\right)\left[8-3\right] = 45
\][/tex]
