Understanding Rational Exponents and Simplification

The video tutorial explains how to rewrite radical expressions using rational exponents and simplify them. It begins by introducing the concept of roots and their equivalence to fractional exponents. The tutorial then applies exponent rules to simplify a given expression, demonstrating each step clearly. The final result is a simplified expression, showcasing the power of understanding and applying exponent rules.

What is the first step in rewriting a radical expression using rational exponents?

• Convert the expression to a fraction.

• Divide the expression by its root.

• Multiply the expression by itself.

• Identify the root and express it as a power.

How can the nth root of a number be expressed using exponents?

• As the number raised to the power of n.

• As the number raised to the power of 1/n.

• As the number multiplied by n.

• As the number divided by n.

What is the equivalent expression for the fourth root of a product?

• The product raised to the power of 4.

• The product raised to the power of 1/4.

• The product divided by 4.

• The product multiplied by 4.

When simplifying a product raised to an exponent, what should be done first?

• Divide the exponents.

• Multiply the exponents.

• Add the exponents.

• Raise each factor to the exponent.

What is the simplified form of a to the fourth power raised to the 1/4 power?

• a to the power of 1

• a to the power of 4

• a to the power of 16

• a to the power of 1/4

What is the relationship between raising a power to another power?

• Add the exponents.

• Divide the exponents.

• Multiply the exponents.

• Subtract the exponents.

What is the simplified form of 5 to the 1/4 power?

• 5 to the power of 4

• 5 to the power of 1

• The fourth root of 5

• 5 to the power of 1/2

How is b to the 12th power raised to the 1/4 power simplified?

• b to the power of 3

• b to the power of 12

• b to the power of 48

• b to the power of 1/4

What is the final simplified form of the expression?

• a to the fourth power, b to the third power

• a, b to the third power times the fourth root of 5

• a, b to the twelfth power

• a to the first power, b to the fourth power

What is the key property used to simplify the expression in the video?

• The quotient of powers property.

• The product of powers property.

• The power of a quotient property.

• The power of a product property.