Order of Operations with Exponents - Pre Algebra

1. Evaluate $(-3)^2$.

   9. The parentheses make $-3$ the base: $(-3)(-3) = 9$.

2. In what order are operations performed in a numerical expression?

   Grouping symbols, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

3. Evaluate $12 \div 2 \times 3$.

   18. Multiplication and division are done left to right: $6 \times 3 = 18$.

4. What does $4^3$ mean, and what is its value?

   $4 \cdot 4 \cdot 4 = 64$. The exponent tells how many times the base is used as a factor.

5. Evaluate $20 - 4^2 \div 2$.

   12. $4^2 = 16$, then $16 \div 2 = 8$, then $20 - 8 = 12$.

6. Evaluate $(1 + 3)^2 \times 3 - 6^2 \div 4$.

   39. $16 \times 3 = 48$ and $36 \div 4 = 9$, so $48 - 9 = 39$.

7. Evaluate $3 + 2^3$.

   11. Evaluate the exponent first: $2^3 = 8$, then $3 + 8 = 11$.

8. Evaluate $-3^2$.

   $-9$. The exponent applies only to 3, and the negative is applied after: $-(3^2) = -9$.

9. Evaluate $(3 + 2)^2$.

   25. Parentheses first: $5^2 = 25$.

10. Evaluate $\frac{2^4 - 6}{5}$.

    2. The fraction bar groups the numerator: $16 - 6 = 10$, and $10 \div 5 = 2$.

11. Evaluate $2 \cdot 3^2$.

    18. The exponent applies only to 3: $2 \cdot 9 = 18$.

12. Evaluate $10 - (1 + 2)^2$.

    1. $(3)^2 = 9$, then $10 - 9 = 1$.

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