CCSS.Math.Content.HSN-RN.A
The standard
Extend the properties of exponents to rational exponents.
Common Core State Standards for Mathematics
What this standard means
Students need to connect roots and powers. They should read a fractional exponent as a root, a power, or both, then rewrite expressions in equivalent forms. They also need to use exponent rules with rational exponents, including products, quotients, powers of powers, and negative exponents.
Mastery looks like moving flexibly between radical and exponent form, such as rewriting cube root of x squared as x^(2/3), then simplifying correctly. Students often get stuck on the denominator as the root, negative exponents, and applying old exponent rules to fractions without checking domain issues.
Ways to teach it
- Use index cards with radical forms, exponent forms, and simplified forms, then have students sort and match equivalent expressions in pairs.
- Ask students to explain which is easier to simplify, radical form or rational exponent form, using three worked examples.
- Give a five-question exit ticket rewriting expressions both ways and simplifying one product with rational exponents.
- Connect rational exponents to side lengths by finding the edge of a cube with volume x^2 using cube roots and exponents.
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Related standards
- CCSS.Math.Content.HSN-RN.A.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notat...
- CCSS.Math.Content.7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- CCSS.Math.Content.HSN-RN.B
Use properties of rational and irrational numbers.
- CCSS.Math.Content.HSN-RN.A.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents.