Answer :

GinnyAnswer
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].

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