Exploring Rational Exponents and Their Properties

This video tutorial covers rational exponents and properties of exponents. It begins with an introduction to rational exponents and their applications. The lesson then explains how to convert radicals into rational exponents, followed by using the product of powers property to solve equations. The tutorial also addresses solving equations with different base numbers and handling negative exponents and fractions. Finally, it discusses the quotient of powers property. Throughout the video, students are encouraged to practice and apply these concepts to solve various equations.

How do you convert a square root into a rational exponent?

• Multiply the exponent by the root number

• Raise the base to the power of 1/2

• Divide the exponent by the root number

• Raise the base to the power of 2

What is the third root of 8 in rational exponent form?

• 8 raised to the 1/3 power

• 8 raised to the 3/2 power

• 8 raised to the 2/3 power

• 8 raised to the 3 power

How do you solve equations with the same base using exponents?

• Multiply the exponents

• Subtract the exponents

• Add the exponents

• Divide one exponent by the other

What is the result of adding x/2 and x/3 when solving an equation with rational exponents?

• 5x/6

• x/5

• 3x/4

• 2x/5

How can you solve an equation when the bases are different numbers?

• Multiply the bases together

• Convert them to have the same base

• Subtract one base from the other

• Convert them to have the same exponent

What is the solution when you have a fraction with a negative exponent?

• Divide the base by the exponent

• Convert the fraction to a positive exponent

• Set the exponents equal to each other

• Multiply the exponent by -1

What is the area of a square blanket if its side is the square root of 8 yards?

• 4 square yards

• 64 square yards

• 16 square yards

• 8 square yards

How do you apply the quotient of powers property to solve equations?

• Add the exponents

• Subtract the exponents

• Multiply the exponents

• Divide the exponents

What is the result of 2 raised to the x divided by 3 over 2 raised to 1 divided by 3?

• 2 raised to the (x+1)/3

• 2 raised to the x/3

• 2 raised to the x

• 2 raised to the (x-1)/3

What step is necessary when the bases in an equation do not match?

• Convert them to have the same base

• Add the bases together

• Convert them to have the same exponent

• Subtract the smaller base from the larger base