Florida B.E.S.T. MA.912.NSO.1.1
The Standard
Extend previous understanding of the Laws of Exponents to include rational exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions involving rational exponents.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite rational exponents as radicals and radicals as rational exponents. They apply exponent rules to evaluate numbers and produce equivalent forms.
What Mastery Looks Like
- A student can evaluate 27^(2/3) as 9 and explain what the 2 and 3 represent. They correctly apply product, quotient, power, zero, and negative exponent rules with rational exponents.
Common Misconceptions
- Students may reverse the numerator and denominator, reading 16^(3/4) as the fourth power of the cube root. They may multiply exponents when powers are multiplied, or treat a negative exponent as a negative value.
How to Assess It
- Exit ticket: Evaluate 16^(3/4), then simplify 8^(2/3) × 8^(1/3). Require one intermediate step for each answer.
Lesson moves
Ways to Teach It
Give pairs cards showing rational powers, radical forms, and values, then have them build matching sets and explain each match.
Ask students to write why 16^(3/4) equals 8, naming the role of the numerator and denominator.
Run a matching relay where teams pair expressions such as 9^(1/2) × 9^(3/2) with simplified values.
Use s = V^(1/3) to calculate cube side lengths for package volumes of 64, 125, and 216 cubic units.
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Printable MA.912.NSO.1.1 Worksheet
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Related Standards
- MA.8.NSO.1.3
Extend previous understanding of the Laws of Exponents to include integer exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate ...
- MA.7.NSO.1.1
Know and apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to whole-number exponents and rati...
- MA.912.NSO.1.3
Generate equivalent algebraic expressions involving radicals or rational exponents using the properties of exponents.
- MA.8.AR.1.1
Apply the Laws of Exponents to generate equivalent algebraic expressions, limited to integer exponents and monomial bases.
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