Simplifying Expressions with Rational Exponents and Radical Forms

The video tutorial explains how to simplify expressions using rational exponents and convert them into radical form. It begins by rewriting the denominator with rational exponents, followed by dividing expressions and subtracting exponents. The tutorial then demonstrates calculating differences in exponents using common denominators. It proceeds to express the simplified expression in radical form and simplifies the radicand by identifying factors raised to the ninth power. The tutorial concludes with the final simplification, showing the equivalence of expressions in both rational and radical forms.

What is the first step in simplifying the given expression using rational exponents?

• Convert the numerator to rational exponents

• Multiply the exponents of the denominator

• Convert the denominator to rational exponents

• Add the exponents of the numerator

When dividing expressions with the same base, what operation is performed on the exponents?

• Subtract the exponents

• Divide the exponents

• Multiply the exponents

• Add the exponents

What is the least common denominator used to calculate the difference in exponents for x?

• 7

• 10

• 8

• 9

How is the expression x^19/9 expressed in radical form?

• x^9 times 9th root

• 9th root of x^9

• x^19 times 9th root

• 9th root of x^19

How many factors of x^9 are in x^19?

• 1

• 2

• 3

• 4

What is the remainder when 29 is divided by 9?

• 4

• 3

• 2

• 1

What is the simplified expression in radical form?

• x^3 y^3 times the 9th root of x y^2

• x^3 y^2 times the 9th root of x y^3

• x^2 y^2 times the 9th root of x y^3

• x^2 y^3 times the 9th root of x y^2

How many factors of y^9 are in y^29?

• 2

• 5

• 3

• 4

What is the equivalent expression using rational exponents?

• x^29/9 y^19/9

• x^9/29 y^9/19

• x^9/19 y^9/29

• x^19/9 y^29/9

What operation is performed to simplify x^9 in the radical form?

• Add 9 to the exponent

• Simplify to one factor of x

• Divide by 9

• Multiply by 9