Exponents and Radicals
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalExponents and radicals run on a short set of rules: multiplying like bases adds the exponents, dividing subtracts them, a power of a power multiplies them, and a power or a root spreads across a product, never across a sum. The algebra is short. The points leak in four moves: a power or root spread across a sum, a negative or fractional exponent misread, like bases combined by the wrong rule, and a correct solve with the wrong value handed back.
These patterns aren't really about whether you know the exponent laws. They're about whether the cross term survived the square, whether a negative exponent stayed a reciprocal instead of becoming a sign, whether each operation got its own rule and not a neighboring one, and whether you reported the exact quantity the item asked for.
The work
4 ways in · any order
Lesson
Exponents and Radicals
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Add, subtract, and multiply exponents by the right rule, keep a power or root from spreading across a sum, and read negative and fractional exponents as reciprocals and roots. The lesson works the rules and the four patterns that derail them, and it saves the trap for last: the equation solved right and the wrong piece handed back.
Diagnostic
10-item topic check
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Ten items across the four patterns: spreading a power or root across a sum, misreading a negative or fractional exponent, combining powers by the wrong rule, and reporting the wrong quantity from a power or radical equation. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
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About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.