Let's simplify the expression [tex]\(10\left[4 \cdot 10 \div(6^2-4^2)+1\right]\)[/tex] step by step.
1. Simplify the exponents:
[tex]\[
6^2 = 36
\][/tex]
[tex]\[
4^2 = 16
\][/tex]
2. Subtract the results of the exponents:
[tex]\[
36 - 16 = 20
\][/tex]
3. Multiply inside the bracket:
[tex]\[
4 \cdot 10 = 40
\][/tex]
4. Divide the multiplication result by the subtraction result:
[tex]\[
40 \div 20 = 2.0
\][/tex]
5. Add 1 to the division result:
[tex]\[
2.0 + 1 = 3.0
\][/tex]
6. Multiply the addition result by 10:
[tex]\[
10 \cdot 3.0 = 30.0
\][/tex]
Therefore, the simplified result of the expression [tex]\(10\left[4 \cdot 10 \div(6^2-4^2)+1\right]\)[/tex] is [tex]\(\boxed{30}\)[/tex].
