Rational Exponents and Radical Forms

The video tutorial explains rational exponents, which are exponents with fractions, as a way to express radical numbers. It covers how to convert between exponents and radicals, with the numerator representing the power and the denominator representing the root. Several examples are provided to illustrate these concepts, including rewriting expressions like 2^(2/3) and 4^(1/2). The tutorial emphasizes understanding the roles of the numerator and denominator in rational exponents.

What is a rational exponent?

• An exponent that is a whole number

• An exponent that is a fraction

• An exponent that is negative

• An exponent that is zero

How can x^(n/d) be expressed in radical form?

• As the nth power of x raised to d

• As the dth root of x raised to n

• As the nth root of x raised to d

• As the dth power of x raised to n

What is 2^(2/3) equivalent to in radical form?

• The square root of 2 squared

• The cube root of 2 squared

• The cube root of 4

• The square root of 4

What is the radical form of 4^(1/2)?

• 4 raised to the power of 2

• The square root of 4

• The cube root of 4

• 4 raised to the power of 1

How is x^(3/2) expressed in radical form?

• The square root of x squared

• The square root of x cubed

• The cube root of x squared

• The cube root of x cubed

What is the radical form of y^(0.5)?

• The square root of y

• y raised to the power of 2

• The cube root of y

• y raised to the power of 0.5

How can m^(p/3) be expressed in radical form?

• The square root of m cubed

• The cube root of m squared

• The cube root of m raised to p

• The square root of m raised to p

In a rational exponent, what does the numerator represent?

• The power to which the base is raised

• The base itself

• The reciprocal of the base

• The root of the base

In a rational exponent, what does the denominator represent?

• The reciprocal of the base

• The root or index of the radical

• The base itself

• The power to which the base is raised

What is the general rule for converting rational exponents to radicals?

• The numerator is the root, and the denominator is the power

• Both numerator and denominator are roots

• The numerator is the power, and the denominator is the root

• Both numerator and denominator are powers