ACT Preparation / Unit 7 ACT 0607 worked example, 60 to 90 seconds
Simplifying With Exponent Rules
The idea
To simplify an expression with several exponents, work in four steps. First, apply any power of a product or quotient to each factor inside. Second, combine powers of the same base: add exponents when multiplying, subtract when dividing. Third, rewrite negative exponents as reciprocals, moving the factor across the fraction bar. Fourth, simplify the numbers.
In practice
Worked example: simplify (2x³y⁻²)² ÷ (4x²y). Step one: (2x³y⁻²)² = 4x⁶y⁻⁴. Step two: 4x⁶y⁻⁴ ÷ 4x²y = x⁴y⁻⁵, because 6 − 2 = 4 and −4 − 1 = −5. Step three: y⁻⁵ moves below the bar, giving x⁴/y⁵. Step four: the 4s have cancelled, so the result is x⁴ over y⁵.
Where people slip
Move only the factor that carries the negative exponent, not its whole term. In 3x⁻², the 3 stays in the numerator: 3x⁻² = 3/x², not 1/(3x²).
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