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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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## Rational Exponents

### Lesson 7 Contents

Example 2Exponential Form

Example 3Evaluate Expressions with Rational Exponents

Example 4Rational Exponent with Numerator Other Than 1

Example 5Simplify Expressions with Rational Exponents

Definition of

Definition of

### Example 7-1b

Write each expression in radical form.

a.

b.

### Example 7-1c

Write using rational exponents.

Definition of

### Example 7-2a

Write using rational exponents.

Definition of

### Example 7-2b

Write each radical using rational exponents.

a.

b.

Evaluate

Simplify.

### Example 7-3a

Evaluate.

Power of a Power

Expand the square.

Find the fifth root.

### Example 7-3c

Evaluate each expression.

a.

b.

### Example 7-3e

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.

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.

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:The formula prediction is slightly higher than hisactual total.

Simplify.

Multiply powers.

Simplify.

Multiply by

### Example 7-5c

Simplify each expression.

a.

b.

### Example 7-5d

Simplify.

Rational exponents

Power of a Power

### Example 7-6a

Quotient of Powers

Simplify.

### Example 7-6b

Simplify.

Rational exponents

Power of a Power

Multiply.

Simplify.

Simplify.

is the conjugate

of

Multiply.

### Example 7-6d

Simplify each expression.

a.

b.

c.