π
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y = mx+b
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About this video
Worked examples applying the exponent laws to simplify expressions — multiplying, dividing and raising powers to powers.
What it covers
- Rule 1: multiplying the same base — add the exponents
- Rule 2: dividing the same base — subtract the exponents
- Rule 3: change numbers to the same base, in brackets (25 = 5²)
- Rule 4: an exponent outside a bracket multiplies every exponent inside
- Negative exponents move to the denominator; a zero exponent gives 1
- A minus between two terms: take out a common factor
Extra worked examples
✍️ Extra example: simplify (2a²b)³ · ab⁴ ÷ 4a⁵b³
- 1(2a²b)³ = 2³a⁶b³ = 8a⁶b³Rule 4: the 3 multiplies every exponent inside — the 2 as well.
- 28a⁶b³ · ab⁴ = 8a⁷b⁷Rule 1: a has an exponent of 1, so 6 + 1 = 7; and 3 + 4 = 7.
- 38a⁷b⁷ ÷ 4a⁵b³ = 2a²b⁴Numbers first (8 ÷ 4 = 2), then Rule 2: subtract the exponents.
✍️ Extra example: simplify (5n + 1 − 5n)/5n
- 1(5n(5 − 1))/5nA minus between the terms — no rule applies across it, so take out the common factor 5ⁿ.
- 2= 4Now 5ⁿ is a factor top and bottom and cancels.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Simplify a⁵ · a³.
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a⁸ (Rule 1) - 2Simplify (y²)⁴.
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y⁸ (Rule 4) - 3Simplify 12x⁵y²/4x²y⁵ and leave positive exponents.
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3x³y−3 = 3x³/y³ - 4Simplify (25x · 5)/(52x + 1).
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((5²)x · 51)/(52x + 1) = (52x + 1)/(52x + 1) = 1 - 5Simplify (3n + 2 − 3n)/(8 · 3n).
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(3n(9 − 1))/(8 · 3n) = 1
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