Certainly! Let's simplify the given expression step by step:
[tex]\[ 5 \cdot 13 \left[6^2 \div (5^2 - 4^2) + 9\right] \][/tex]
1. Simplify the innermost parentheses:
[tex]\[ 5^2 - 4^2 \][/tex]
[tex]\[ 25 - 16 = 9 \][/tex]
2. Substitute this value back into the expression:
[tex]\[ 5 \cdot 13 \left[6^2 \div 9 + 9\right] \][/tex]
3. Calculate \( 6^2 \):
[tex]\[ 6^2 = 36 \][/tex]
4. Perform the division inside the brackets:
[tex]\[ 36 \div 9 = 4 \][/tex]
5. Add 9 to the result of the division:
[tex]\[ 4 + 9 = 13 \][/tex]
6. Now we have:
[tex]\[ 5 \cdot 13 \cdot 13 \][/tex]
7. First, perform the multiplication inside the brackets:
[tex]\[ 13 \cdot 13 = 169 \][/tex]
8. Finally, multiply by 5:
[tex]\[ 5 \cdot 169 = 845 \][/tex]
So, the simplified value of the expression is:
[tex]\[ 845 \][/tex]
