Rational ExponentsN.RN.2 – Rewrite expressions involving radicals and rational

exponents using properties of exponents.N.RN.3 – Explain why the sum or product of two rational

numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero

rational number and an irrational number is irrational.

How to play…

• When a new problem is shown, write down your answer on a slip of paper (write it BIG)

• Do not show your answer to anyone!

• When the teacher says “SHOWDOWN” slap your answer down for everyone to see.

• Discuss your answers with your group, come to an agreement on the correct answer

Showdown

(-

… what is x?

Rational:

Integer:

Whole:

Natural:

Irrational:

Sets of Real Numbers

Always, Sometimes, Never

1. The sum of two rational numbers is rational2. The product of two rational numbers is a whole

number 3. The sum of a rational number and an irrational

number is rational4. The product of a nonzero rational number and

an irrational number is irrational

Always, Sometimes, Never

1. The sum of two rational numbers is rational (A)2. The product of two rational numbers is a whole

number (S)3. The sum of a rational number and an irrational

number is rational (N)4. The product of a nonzero rational number and

an irrational number is irrational (A)

Properties of ExponentsName Property Example

Product of Powers

Quotient of Powers

Power of a Product

Power of a Quotient

Power of a Power

Negative Exponent

The “nth” root of a

𝑛√𝑎RadicandIndex

Properties of RadicalsName Property Example

Radical of a Product

Radical of a Quotient

Radical of a Radical

Rational Exponents & RadicalsExponent Radical Example

or

Example 1. Example 2.

With your partner…Explain why it makes sense that and

Example 3: Simplify each expression. Express solutions in radical form (where necessary).

Example 4.

In parts B & C, you started with an expression in radical form, converted to rational exponent form, and then converted back to radical form. Explain the purpose of each conversion.

Example 5.

B) What is the simplified form of ? How is it related to ?

Example 6.

Example 6.

D)

E)

F)

Example 6.

G)

H)

Exit Card

1) A) B)

C) D)

2) What are rational and irrational numbers and

how are radicals related to rational exponents?