Order of Operations - SSAT Upper Level Quantitative

1. What is the value of $\left(2^3\right)^2$ using order of operations?

   $64$. Parentheses first: $2^3 = 8$, then raise to the power of 2.

2. What is the value of $2\left(3 + 5\right) - 4$ using order of operations?

   $12$. Parentheses first: $3 + 5 = 8$, multiply by 2 to get 16, then subtract 4.

3. What is the value of $(6 + 2) \times 5$ using order of operations?

   $40$. Parentheses first: $6 + 2 = 8$, then multiply by 5.

4. What is the value of $4 - \{2 + [3 - (1)]\}$ using order of operations?

   $0$. Evaluate innermost first: (1), then [3-1]=2, {2+2}=4, subtract from 4.

5. What is the value of $18 \div 3 \times 2$ using left-to-right for $\div$ and $\times$?

   $12$. Division and multiplication from left to right: $18 \div 3 = 6$, then $6 \times 2$.

6. What is the value of $2^{3^2}$ using order of operations?

   $512$. Exponents are evaluated from right to left: $3^2=9$, then $2^9=512$.

7. What is the value of $6 + 2 \times 5$ using order of operations?

   $16$. Multiplication first: $2 \times 5 = 10$, then add 6.

8. What is the value of $(-3)^2$ using order of operations?

   $9$. Parentheses include the negative: $-3$ squared is 9.

9. What is the value of $7 + 2\left[5 - 3(1)\right]$ using order of operations?

   $11$. Innermost parentheses: $3(1)=3$, subtract from 5 to get 2, multiply by 2, add to 7.

10. What is the value of $5 - \left(\frac{3}{4} \times 8\right)$ using order of operations?

    $-1$. Parentheses first: $\frac{3}{4} \times 8 = 6$, then subtract from 5.

11. What is the value of $\frac{18}{3} \times 2$ using order of operations?

    $12$. Division and multiplication left to right: $\frac{18}{3} = 6$, then multiply by 2.

12. What is the value of $3^2 + 4 \times 2$ using order of operations?

    $17$. Exponent first: $3^2=9$, then multiply $4 \times 2=8$, add them.

13. What is the correct order of operations for evaluating $6 + 2 \times 5$?

    Multiply first, then add. Follow PEMDAS: perform multiplication before addition.

14. What is the value of $12 - 3\left(2 + 1\right)$ using order of operations?

    $3$. Parentheses first: $2 + 1 = 3$, multiply by 3 to get 9, subtract from 12.

15. What is the value of $\frac{1}{2} \times 8 + 3$ using order of operations?

    $7$. Multiplication before addition: $\frac{1}{2} \times 8 = 4$, then add 3.

16. What is the value of $\left(\frac{3}{5} + \frac{2}{5}\right) \times 10$ using order of operations?

    $10$. Parentheses first: $\frac{3}{5} + \frac{2}{5} = 1$, then multiply by 10.

17. What is the value of $18 \div (3 \times 2)$ using order of operations?

    $3$. Parentheses first: $3 \times 2 = 6$, then divide 18 by 6.

18. What is evaluated first in $3^2 + 4 \times 2$ according to order of operations?

    The exponent $3^2$. Exponents are evaluated before multiplication and addition.

19. What is the value of $\frac{18}{3 \times 2}$ using order of operations?

    $3$. Multiplication in denominator first: $3 \times 2 = 6$, then $18 \div 6$.

20. What is the value of $2\left(3 + 5\right)^2$ using order of operations?

    $128$. Parentheses first: $3 + 5 = 8$, square to 64, then multiply by 2.

21. What is the value of $9 - \left[6 - \left(2^2\right)\right]$ using order of operations?

    $7$. Innermost exponent: $2^2=4$, subtract from 6 to get 2, then subtract from 9.

22. What is the value of $20 - 6 + 3$ using left-to-right for $+$ and $-$?

    $17$. Subtraction and addition from left to right: $20 - 6 = 14$, then add 3.

23. What is the value of $-3^2$ using order of operations (no parentheses)?

    $-9$. Exponent first: $3^2 = 9$, then apply the negative sign.

24. What is the value of $24 \div 6 + 2 \times 3$ using order of operations?

    $10$. Division and multiplication first: $24 \div 6 = 4$ and $2 \times 3 = 6$, then add.

25. What is the value of $| -7 + 2 \times 3 |$ using order of operations?

    $1$. Multiplication first: $2 \times 3 = 6$, add to -7 to get -1, then absolute value.

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