UNIT 8 LESSON 1

RADICALS AND RATIONAL

EXPONENTS

COLLEGE PREP

OBJECTIVES

• Evaluate 𝑛th roots

• Simplify expressions of the form 𝑛𝑎𝑛

• Evaluate expressions of the form 𝑎1

𝑛

• Evaluate expressions of the form 𝑎𝑚

𝑛

PARTS OF A RADICAL

𝑛 𝑥ROOT/INDEX

RADICAND

EVALUATING “PERFECT” RADICALS

Evaluate the following:

A.327 B.

4256

C.3−125 D.

416

EVALUATING “PERFECT” RADICALS

Evaluate the following:

E.5𝑧5 F.

4𝑛 − 4 4

G. −62 6 H.

3 33

23

RATIONAL EXPONENTS AS RADICALS

𝑎1𝑛 =

𝑛𝑎1

RATIONAL EXPONENTS AS RADICALS

𝑎1𝑛 = 𝑛 𝑎

Rewrite the following radicals with a rational exponent.

I. 5 𝑥 J.39𝑧 K.

4 𝑎3𝑏

7

RATIONAL EXPONENTS AS RADICALS

𝑎𝑚𝑛 =

𝑛𝑎𝑚

RATIONAL EXPONENTS AS RADICALS

𝑎𝑚𝑛 =

𝑛𝑎𝑚

Rewrite the expression in radical form.

L. 93

2 M. 1252

3

N. −363

2 O. −274

3

RATIONAL EXPONENTS AS RADICALS

𝑎𝑚𝑛 =

𝑛𝑎𝑚

Evaluate the following expressions.

L. 93

2 M. 1252

3

N. −363

2 O. −274

3

RATIONAL EXPONENTS AS RADICALS

𝑎𝑚𝑛 =

𝑛𝑎𝑚

Rewrite the following with Rational Exponents

P. 5𝑥3 Q. 2

3𝑎2

R. 324𝑥𝑦2

4

RATIONAL EXPONENTS AS RADICALS

Completely simplify (no negative exponents)

S. 49−1

2 T. 1

64−23

U. 3𝑥 −3

4

OBJECTIVES

• Evaluate 𝑛th roots

• Simplify expressions of the form 𝑛𝑎𝑛

• Evaluate expressions of the form 𝑎1

𝑛

• Evaluate expressions of the form 𝑎𝑚

𝑛

HOMEWORK

In Class Assignment C8.1

Homework H8.1

EDPuzzle Q8.1