Exploring Rational Exponents and Exponent Properties

This video tutorial covers the properties of rational exponents and their relationship with radicals. It explains how to solve equations involving rational exponents by matching bases and exponents, and how to simplify such equations using division. The tutorial provides step-by-step examples and encourages students to practice solving similar problems on their own.

What is a rational exponent?

• An exponent that is always positive

• An exponent that includes a fraction and/or a variable expression

• An exponent that is always negative

• An exponent that is a whole number

How can the square root of 4 be expressed as a rational exponent?

• 4 to the power of 3

• 4 to the power of 1/4

• 4 to the power of 1/2

• 4 to the power of 2

What is the rational exponent form of the sixth root of 7 squared?

• 7 to the power of 3

• 7 to the power of 6/2

• 7 to the power of 1/3

• 7 to the power of 2/6

When multiplying terms with the same base, what should you do with the exponents?

• Subtract the exponents

• Add the exponents

• Multiply the exponents

• Divide the exponents

How do you solve 3^(x/2) * 3^(x/3) = 3^9?

• Subtract the exponents

• Add the exponents and set them equal to 9

• Divide the exponents

• Multiply the exponents

What should you do if the bases are not the same in an equation?

• Ignore the bases

• Add the bases

• Subtract the bases

• Find a common base and rewrite the equation

How can you rewrite 27 as a base of 3?

• 3^2

• 3^3

• 3^4

• 3^5

What is the reciprocal of 1/3?

• 3/1

• 3

• 1/3

• 1

How do you get rid of an exponent in an equation?

• Multiply by the exponent

• Subtract the exponent

• Divide by the exponent

• Raise to the reciprocal power

What is the final step in solving an equation with matching exponents?

• Divide the exponents

• Multiply the exponents

• Set the exponents equal to each other

• Add the exponents