Standard #: MAFS.912.N-RN.1.2 (Archived Standard)

Students are asked to rewrite expressions involving radicals and rational exponents in equivalent forms.

Students are asked to convert numerical expressions from exponential to radical form.

Students are asked to convert a product of a radical and exponential expression to a single power of two.

Students are asked to convert numerical expressions from radical to exponential form.

Students will simplify and perform operations on radical expressions. Pairs of students will work on problems at different complexity levels that lead to the same solution. The students will challenge each other to prove their solutions are correct. This activity does not address rational exponents.

This lesson unit is intended to help you assess how well students are able to:

• Use the properties of exponents, including rational exponents, and manipulate algebraic statements involving radicals.
• Discriminate between equations and identities.

There is also an opportunity to consider the role of the imaginary number , but this is optional.

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Learn to rewrite products involving radicals and rational exponents using properties of exponents in this interactive tutorial.

In this example, students use properties of rational exponents and other algebraic concepts to compare and verify the relative size of two real numbers that involve decimal exponents.

This makes for a good follow-up task on rational irrational numbers after the students have been acquainted with some of the more basic properties, asking students to reason about rational and irrational numbers (N-RN.3) in a variety of ways. In addition to eliciting several different types of reasoning, the task requires students to rewrite radical expressions in which the radicand is divisible by a a perfect square.

This tutorial demonstrates how to use the power of a power property with both numerals and variables.

Exponents are not only integers and unit fractions. An exponent can be any rational number expressed as the quotient of two integers.

Radical expressions can often be simplified by moving factors which are perfect roots out from under the radical sign.

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Learn to rewrite products involving radicals and rational exponents using properties of exponents in this interactive tutorial.

In this example, students use properties of rational exponents and other algebraic concepts to compare and verify the relative size of two real numbers that involve decimal exponents.

This tutorial demonstrates how to use the power of a power property with both numerals and variables.

Exponents are not only integers and unit fractions. An exponent can be any rational number expressed as the quotient of two integers.

Radical expressions can often be simplified by moving factors which are perfect roots out from under the radical sign.

In this example, students use properties of rational exponents and other algebraic concepts to compare and verify the relative size of two real numbers that involve decimal exponents.

This tutorial demonstrates how to use the power of a power property with both numerals and variables.