Pre-Algebra 30 - Rational Exponents

The video tutorial by Professor Von Schmohawk explores the concept of rational exponents, demonstrating how exponents can be fractions and how they can be evaluated in different ways. It explains the equivalence of operations involving cube roots and squaring, and introduces negative rational exponents. The tutorial also covers simplifying radical expressions using rational exponents, providing examples to illustrate these concepts.

What does a fractional exponent with a numerator of 1 represent?

• The reciprocal of the number

• The n-th root of the number

• The cube of the number

• The square of the number

When evaluating a fractional exponent, which method is generally easier?

• Multiplying the base by itself

• Taking the root first, then squaring

• Dividing the base by the exponent

• Squaring first, then taking the root

What does a negative rational exponent indicate?

• The number is zero

• The reciprocal of the number with a positive exponent

• The number is negative

• The number is imaginary

How can you simplify 1 over the square root of x using exponents?

• x to the power of 1/2

• x to the power of -1/2

• x to the power of 2

• x to the power of -2

What is the simplified form of a over the square root of a?

• The square root of a

• a to the power of 1/2

• a to the power of 2

• a to the power of -1/2

How do you express the square root of a over the cube root of a using exponents?

• a to the power of 1/3

• a to the power of 2/3

• a to the power of 1/6

• a to the power of 1/2

What is the result of simplifying the cube root of a squared over the sixth root of a?

• a to the power of 1/6

• a to the power of 1/3

• a to the power of 1/2

• a to the power of 2/3