Understanding Exponents and Their Properties

The video tutorial covers the basics of exponents, including positive, negative, and fractional exponents. It explains how to interpret fractional exponents as roots, such as square roots and cube roots, and demonstrates this with examples. The tutorial also introduces the concept of rational exponents and their properties, highlighting the patterns and symmetry in exponentiation.

What is the result of 4 raised to the third power?

• 12

• 16

• 64

• 32

How do you interpret a negative exponent, such as 4 to the negative 3 power?

• Multiply by 4 three times

• Take the reciprocal of 4 to the third power

• Subtract 4 three times

• Divide by 4 three times

What is 4 to the 1/2 power equivalent to?

• Cube root of 4

• 2

• 4

• Square root of 4

What is the principal square root of 9?

• 5

• 4

• 3

• 2

What is 25 to the 1/2 power?

• 7

• 6

• 4

• 5

What does 8 to the 1/3 power represent?

• Fifth root of 8

• Square root of 8

• Cube root of 8

• Fourth root of 8

What is the cube root of 64?

• 5

• 2

• 4

• 3

What is 32 to the 1/5 power?

• 2

• 5

• 3

• 4

Which of the following is equivalent to 32?

• 2 to the fourth power

• 3 to the fifth power

• 4 to the third power

• 2 to the fifth power

What is the result of raising a number to a fractional exponent?

• It becomes a fraction

• It becomes a negative number

• It becomes a root of the number

• It becomes a larger number