Question
simplify the expression.
13 [6² ÷ (5² - 4/²) + 9]
13 [6² ÷ (5² - 4/²) + 9]
Answers
GPT-4o mini
To simplify the expression \( 13 [6^2 ÷ (5^2 - 4^2) + 9] \), we will follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).
1. Calculate the exponents:
- \( 6^2 = 36 \)
- \( 5^2 = 25 \)
- \( 4^2 = 16 \)
2. Substitute these values back into the expression:
\[
13 [36 ÷ (25 - 16) + 9]
\]
3. Calculate the expression inside the parentheses:
\[
25 - 16 = 9
\]
4. Substitute this value back:
\[
13 [36 ÷ 9 + 9]
\]
5. Perform the division:
\[
36 ÷ 9 = 4
\]
6. Now substitute back:
\[
13 [4 + 9]
\]
7. Add the values inside the brackets:
\[
4 + 9 = 13
\]
8. Finally, calculate:
\[
13 \times 13 = 169
\]
The simplified expression is:
\[
\boxed{169}
\]
1. Calculate the exponents:
- \( 6^2 = 36 \)
- \( 5^2 = 25 \)
- \( 4^2 = 16 \)
2. Substitute these values back into the expression:
\[
13 [36 ÷ (25 - 16) + 9]
\]
3. Calculate the expression inside the parentheses:
\[
25 - 16 = 9
\]
4. Substitute this value back:
\[
13 [36 ÷ 9 + 9]
\]
5. Perform the division:
\[
36 ÷ 9 = 4
\]
6. Now substitute back:
\[
13 [4 + 9]
\]
7. Add the values inside the brackets:
\[
4 + 9 = 13
\]
8. Finally, calculate:
\[
13 \times 13 = 169
\]
The simplified expression is:
\[
\boxed{169}
\]