Exponent rules for multiplying powers

Same base, multiplying: add the exponents.

The common mistake

Multiplying the exponents (x³ · x⁴ = x¹²) or the bases (2³ · 2² = 4⁵).

Instead: xᵃ · xᵇ = xᵃ⁺ᵇ with the same base kept. Only a power of a power multiplies: (xᵃ)ᵇ = xᵃᵇ.

Worked example with Guide me

Simplify 2x³ · 5x⁴.

Sugar · Multiply the numbers in front first.
Student · 2 × 5 = 10.
Sugar · Same base x — add or multiply exponents?
Student · Add: 3 + 4 = 7.

Answer: 10x⁷

Try 3 practice questions

1. Simplify a² · a⁵.
Show answer
a⁷
2. Simplify (y³)².
Show answer
y⁶
3. Simplify 3x² · 4x.
Show answer
12x³

Quick answers

What is the most common mistake with exponent rules for multiplying powers?: Multiplying the exponents (x³ · x⁴ = x¹²) or the bases (2³ · 2² = 4⁵).
How do I get exponent rules for multiplying powers right?: xᵃ · xᵇ = xᵃ⁺ᵇ with the same base kept. Only a power of a power multiplies: (xᵃ)ᵇ = xᵃᵇ.
Can you show a worked example?: Simplify 2x³ · 5x⁴. 10x⁷

Related concepts

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