Simplifying Expressions and Exponents

The video tutorial explains how to simplify a given rational expression by identifying and simplifying radicals. It demonstrates rewriting radicals using rational exponents and applying exponent rules to simplify the expression further. The process involves recognizing perfect squares, converting radicals to rational exponents, and using exponent multiplication rules. The tutorial concludes with the final simplification of the expression to the value of 27.

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

• Identify the radical that simplifies nicely

• Multiply all terms by 2

• Convert all numbers to decimals

• Add all the exponents

What is the significance of the number 81 in the simplification process?

• It is a prime number

• It is an irrational number

• It is a perfect cube

• It is a perfect square

How can 9 be expressed as a perfect square?

• 2 squared

• 3 squared

• 4 squared

• 5 squared

What does the index of a radical tell us when using rational exponents?

• The power to which the base is raised

• The denominator of the rational exponent

• The base of the expression

• The numerator of the rational exponent

When converting a radical to a rational exponent, what does the exponent inside the radical become?

• The base of the expression

• The coefficient of the expression

• The numerator of the rational exponent

• The denominator of the rational exponent

What operation is performed when powers are raised to powers?

• Divide the exponents

• Multiply the exponents

• Subtract the exponents

• Add the exponents

What is the result of multiplying 3 raised to the 6/5 power by 3 raised to the 9/5 power?

• 3 raised to the 18/5 power

• 3 raised to the 15/5 power

• 3 raised to the 12/5 power

• 3 raised to the 9/5 power

Which of the following is a correct step in simplifying the expression?

• Adding the bases

• Dividing the bases

• Subtracting the exponents

• Multiplying the exponents

What does 15/5 simplify to in the context of this problem?

• 3

• 2

• 5

• 1

What is the final simplified result of the given expression?

• 18

• 27

• 36

• 9