Understanding Fractional Exponents

The video tutorial explains how to interpret and solve problems involving fractional exponents. It begins with a simple example of finding the cube root of 64, then progresses to more complex fractional exponents like 64 to the 2/3 power. The tutorial also covers handling negative exponents using the example of 8/27 raised to the negative 2/3 power, emphasizing the use of exponent properties and reciprocal operations.

What is the cube root of 64?

• 4

• 5

• 3

• 2

How can 64 to the 2/3 power be expressed using the property of exponents?

• 64 to the 1/3 power squared

• 64 to the 1/2 power cubed

• 64 to the 2/3 power directly

• 64 to the 3/2 power squared

What is the property of exponents used to simplify 64 to the 2/3 power?

• Addition of exponents

• Subtraction of exponents

• Multiplication of exponents

• Division of exponents

What is the first step in handling a negative exponent?

• Square the base

• Add 1 to the exponent

• Take the reciprocal of the base

• Multiply the exponent by -1

What is the reciprocal of 8/27?

• 1/27

• 1/8

• 8/27

• 27/8

How can a fraction raised to a power be simplified?

• Raise both the numerator and denominator to the power

• Raise only the denominator to the power

• Multiply the fraction by the power

• Raise only the numerator to the power

What is the cube root of 27?

• 2

• 3

• 4

• 5

What is the result of 8 to the 1/3 power?

• 3

• 4

• 1

• 2

What is the final result of raising 27 to the 2/3 power and 8 to the 2/3 power?

• 2/3

• 9/4

• 4/9

• 3/2

What is the simplified form of 3 squared over 2 squared?

• 9/4

• 2/3

• 4/9

• 3/2