L1 · Powers in Single-Variable Algebraic Terms

Learning goal

“I can read an algebraic term as a coefficient times a power, unfold it into a multiplication, fold a multiplication back into a term, and evaluate a term by substituting a value - computing the power before the coefficient.”

Algebraic term (monomial) — the product of a coefficient and a power, like 4x³. A term is a single chunk of an expression.

Coefficient — the number factor in a term, including its sign: in -4y⁵ the coefficient is -4.

Power — a repeated multiplication written with an exponent: x³ means x · x · x. The variable is the base; the exponent counts the factors.

Expanded form — a term written out as an explicit multiplication: 4x³ expanded is 4 · x · x · x.

Worked example

Take the term 4x³. Step 1: Read it in two parts: a coefficient, 4, and a power, x³. Step 2: The power unfolds: x³ = x · x · x. So the whole term unfolds to 4 · x · x · x - four factors: one number and three copies of the variable. Step 3: Fold it back: count the x factors (three) - that count is the exponent. The number factor stays in front as the coefficient: 4x³. Step 4: Watch the sign travel: -3x² unfolds to (-3) · x · x. The coefficient is -3, not 3 - the sign is part of the coefficient. Say it plainly: an algebraic term is a multiplication that has been folded up. The exponent counts copies of the variable only - it never counts the coefficient.

Check yourself — explain it

In 4x³, why does the exponent 3 not apply to the 4?

Paired problem — example still visible

Unfold 5n⁴ into a multiplication -> 5 · n · n · n · n (coefficient 5, then four n factors)

Faded completion — last step is yours

"7 · a · a = 7a^___" -> 2

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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