NY Next Generation Math AI-A.SSE.3.c

MathGrades 9–12Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

The Standard

Use the properties of exponents to rewrite exponential expressions.

New York State Next Generation Mathematics Learning Standards · Write expressions in equivalent forms to reveal their characteristics.

Teacher's field guide

What Students Need to Do: Students use exponent properties to rewrite Algebra I exponential expressions with integer exponents or linear expressions in the exponent. Rational exponents remain outside this course expectation.
What Mastery Looks Like: The student combines products, quotients, and powers correctly and keeps a linear exponent expression intact. The rewritten form is equivalent and makes a growth feature or calculation simpler.
Common Misconceptions: Students may multiply bases when adding exponents does not apply, distribute an outside exponent over addition, or treat an exponent expression as a coefficient. They may introduce rational exponents prematurely.
How to Assess It: Ask students to rewrite 3^(2x) times 3^(x minus 1) as one power and justify each exponent step.

Lesson moves

Use exponent tiles to combine same-base factors and build the resulting linear exponent.
Ask students why exponent rules apply to products of like bases but not to sums.
Play exponent-law repair with expressions containing one incorrect product, quotient, or power rule.
Rewrite an exponential population or depreciation model to compare equivalent time intervals.

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