💡 What You Will Learn
Order of Operations tells you which part of an expression to solve first. On the GED, expressions like 4(-5)² + 3√4 require you to follow PEMDAS carefully — doing the steps in the wrong order gives the wrong answer. This lesson walks through every rule step by step!
Solve everything inside ( ) before anything else. Treat what's inside parentheses as its own mini-problem.
After parentheses, evaluate all powers (²,³…) and square roots (√). Roots are treated the same as exponents in order of operations.
Work left to right. Neither × nor ÷ takes priority — do whichever comes first from left to right.
Last step, left to right. Neither + nor − takes priority — do whichever comes first from left to right.
"Please Excuse My Dear Aunt Sally"
P=Parentheses, E=Exponents, M=Multiply, D=Divide, A=Add, S=Subtract
In the expression 4(-5)², you must evaluate (-5)² FIRST before multiplying by 4. This is the E in PEMDAS — Exponents come before Multiplication!
In 4(-5)², the exponent is (-5)². It's the part being raised to a power.
(-5)² = (-5) × (-5) = 25
Two negatives multiply to give a positive!
4 × 25 = 100
The 4 in front is the coefficient — you multiply it AFTER solving the exponent.
Evaluate 3(-4)². (Step 1: (-4)² = ? Step 2: 3 × ? = ?)
In the expression 3√4, the square root √4 must be evaluated BEFORE multiplying by 3. Square roots are part of the E step in PEMDAS — treated the same as exponents.
√4 = 2 (because 2 × 2 = 4)
3 × √4 = 3 × 2 = 6
Evaluate 5√9. (Step 1: √9 = ? Step 2: 5 × ? = ?)
(-5)² — the negative IS inside the parentheses, so it gets squared.
-5² — the negative is NOT inside parentheses, so only 5 gets squared, then negated.
These are completely different operations!
(-5)² = (-5) × (-5) = +25
Negative × negative = positive. Answer is POSITIVE.
-5² = -(5²) = -(25) = −25
Only 5 gets squared. Then negate. Answer is NEGATIVE.
What is the difference between (-4)² and -4²? Work them both out!
| Step | PEMDAS | Operation | Result |
|---|---|---|---|
| 1 | E | (-5)² = (-5)×(-5) | 25 |
| 2 | M | 4 × 25 | 100 |
| 3 | E | √4 | 2 |
| 4 | M | 3 × 2 | 6 |
| 5 | A | 100 + 6 | 106 ✅ |
Try a=2, b=3, c=4, d=9 → solve 2(-3)² + 4√9 step by step!