Powers Before Products
Powers before products is an order of operations rule in Grade 8 math (Yoshiwara Core Math) requiring that exponents be evaluated before multiplication. In 3 × 2³, calculate 2³ = 8 first, then 3 × 8 = 24 — not (3×2)³ = 216. This rule is part of PEMDAS/BODMAS: Parentheses → Exponents → Multiplication/Division → Addition/Subtraction. Misapplying the order by multiplying before raising to a power is a common algebra error.
Key Concepts
Property Rule: Compute powers before multiplications or divisions. If we want to multiply before computing the power, we must use parentheses around the product. The parentheses tell us to simplify what’s inside first.
Examples To simplify $5 \cdot 2^3$, you first compute the power $2^3=8$. Then you multiply: $5 \cdot 8 = 40$.
To simplify $(5 \cdot 2)^3$, you first multiply inside the parentheses $5 \cdot 2=10$. Then you compute the power: $10^3 = 1000$.
Common Questions
What does 'powers before products' mean?
Exponents (powers) must be calculated before multiplication (products). In 3 × 2³, calculate 2³ = 8 first, then 3 × 8 = 24.
What is the correct order of operations?
Parentheses → Exponents → Multiplication/Division (left to right) → Addition/Subtraction (left to right). Often remembered as PEMDAS.
What is 5 × 3²?
3² = 9 first, then 5 × 9 = 45.
How does misapplying this lead to errors?
Multiplying before the exponent: (3 × 2)³ = 6³ = 216. Correct: 3 × 2³ = 3 × 8 = 24.
Do parentheses override this rule?
Yes. Parentheses are evaluated first. (3 × 2)³ = 6³ = 216 because parentheses force multiplication before the exponent.