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Rational Exponents. Rational Exponents. Rational Exponents. Lesson 7 Contents. Example 1 Radical Form Example 2 Exponential Form Example 3 Evaluate Expressions with Rational Exponents Example 4 Rational Exponent with Numerator Other Than 1

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Rational Exponents

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Lesson 7 contents l.jpg
Lesson 7 Contents

Example 1Radical Form

Example 2Exponential Form

Example 3Evaluate Expressions with Rational Exponents

Example 4Rational Exponent with Numerator Other Than 1

Example 5Simplify Expressions with Rational Exponents

Example 6Simplify Radical Expressions


Example 7 1a l.jpg

Write in radical form.

Definition of

Answer:

Example 7-1a


Example 7 1b l.jpg

Write in radical form.

Definition of

Answer:

Example 7-1b


Example 7 1c l.jpg

Write each expression in radical form.

a.

b.

Answer:

Answer:

Example 7-1c


Example 7 2a l.jpg

Write using rational exponents.

Answer:

Definition of

Example 7-2a


Example 7 2b l.jpg

Write using rational exponents.

Answer:

Definition of

Example 7-2b


Example 7 2c l.jpg

Write each radical using rational exponents.

a.

b.

Answer:

Answer:

Example 7-2c


Example 7 3a l.jpg

Evaluate

Answer:

Simplify.

Example 7-3a


Example 7 3c l.jpg

Evaluate.

Power of a Power

Expand the square.

Find the fifth root.

Example 7-3c

Answer: The root is 4.


Example 7 3e l.jpg

Evaluate each expression.

a.

b.

Answer:

Example 7-3e

Answer: 8


Example 7 4a l.jpg

Weight LiftingThe formula can be used toestimatethe maximum total mass that a weight lifter of mass B kilograms can lift in two lifts, the snatch and theclean and jerk, combined.

Original formula

Use a calculator.

Example 7-4a

According to theformula, what is the maximum that U.S. WeightlifterOscar Chaplin III can lift if he weighs 77 kilograms?

Answer:The formula predicts that he can lift at most 372 kg.


Example 7 4b l.jpg

Weight LiftingThe formula can be used toestimatethe maximum total mass that a weight lifter of mass B kilograms can lift in two lifts, the snatch and theclean and jerk, combined.

Example 7-4b

Oscar Chaplin’s total in the 2000 Olympics was 355 kg. Compare this to the value predicted by the formula.

Answer:The formula prediction is somewhat higher than his actual total.


Example 7 4c l.jpg

Weight LiftingUse the formula where M is the maximum total mass that a weight lifter of mass B kilograms canlift.

a. According to the formula, what is the maximum that a weight lifter can lift if he weighs 80 kilograms?

b. If he actually lifted 379 kg, compare this to the valuepredicted by the formula.

Example 7-4c

Answer:380 kg

Answer:The formula prediction is slightly higher than hisactual total.


Example 7 5a l.jpg

Simplify.

Multiply powers.

Answer:

Add exponents.

Example 7-5a


Example 7 5b l.jpg

Simplify.

Multiply by

Example 7-5b


Example 7 5c l.jpg

Answer:

Example 7-5c


Example 7 5d l.jpg

Simplify each expression.

a.

b.

Answer:

Answer:

Example 7-5d


Example 7 6a l.jpg

Simplify.

Rational exponents

Power of a Power

Example 7-6a


Example 7 6b l.jpg

Quotient of Powers

Answer:

Simplify.

Example 7-6b


Example 7 6c l.jpg

Simplify.

Rational exponents

Power of a Power

Multiply.

Answer:

Simplify.

Example 7-6c


Example 7 6d l.jpg

Simplify.

is the conjugate

of

Answer:

Multiply.

Example 7-6d


Example 7 6e l.jpg

Simplify each expression.

a.

b.

c.

Answer:

Answer:

Example 7-6e

Answer: 1


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