Rational Exponents and Simplification

The video tutorial covers simplifying expressions with rational exponents. It begins with an introduction to rational exponents, explaining that they are exponents in fractional form. The tutorial then provides several examples demonstrating different laws of exponents, including the product law, power of a power, power of a quotient, and quotient law. Each example is explained step-by-step, showing how to simplify expressions using these laws. The video concludes with a final example and encourages viewers to engage with the content by commenting and subscribing.

What are rational exponents?

• Exponents in decimal form

• Exponents in negative numbers

• Exponents in fractional form

• Exponents in whole numbers

What is the first step in simplifying x^(1/2) * x^(3/2) using the product law?

• Multiply the exponents

• Divide the exponents

• Subtract the exponents

• Add the exponents

What is the simplified form of x^(1/2) * x^(3/2)?

• x^(5/2)

• x^2

• x^3

• x^(4/2)

In the expression x^(2/3) * x^(1/2), what is the first step to simplify it?

• Find the least common denominator

• Multiply the exponents

• Add the exponents

• Subtract the exponents

What is the simplified form of x^(2/3) * x^(1/2)?

• x^(7/6)

• x^(5/6)

• x^(3/6)

• x^(1/6)

How do you simplify (x^16 * y^8)^(1/8)?

• Multiply the exponents by 8

• Divide the exponents by 8

• Multiply the exponents by 1/8

• Add 8 to the exponents

What is the simplified form of (x^16 * y^8)^(1/8)?

• x^2 * y

• x^2 * y^2

• x * y^2

• x * y

What is the first step in simplifying (x^12 * y^6)^(1/6)?

• Multiply the exponents by 6

• Add the exponents

• Multiply the exponents by 1/6

• Divide the exponents by 6

What is the simplified form of (x^12 * y^6)^(1/6)?

• x^2 / y^2

• x^2 / y

• x^2 * y

• x / y^2

How do you simplify x^(3/2) * y^(7/3) / (x^3 * y^(2/9))?

• Add the exponents

• Multiply the exponents

• Subtract the exponents

• Divide the exponents