Exploring Rational Exponents and Their Properties

This video tutorial covers rational exponents and properties of exponents. It begins with an introduction to the topic and a review of key vocabulary such as base, exponent, and power. The lesson then explains rules for simplifying expressions with exponents, including the product of powers, power of a power, and power of a product. It also covers the quotient of powers, zero exponent property, and power of a quotient. The tutorial concludes with a discussion on negative exponents and how to convert them to positive exponents using reciprocals.

What is the term used to describe a number or variable raised to an exponent?

• Coefficient

• Power

• Base

• Product

If you have the expression x^3 * x^2, what is the simplified form of this expression?

• x^6

• x^2

• x^5

• 2x^5

According to the 'Product of Powers' rule, how do you handle powers with the same base?

• Multiply the exponents

• Divide the exponents

• Subtract the exponents

• Add the exponents

What is the result of simplifying the expression (2^3 * 2^4)?

• 2^7

• 6^7

• 8^4

• 2^12

What is the result of (b^3)^4 according to the 'Power of a Power' rule?

• b^6

• b^12

• b^5

• b^7

How do you handle a power raised to another power, such as (3^2)^3?

• 3^5

• 9^3

• 3^6

• 6^3

How do you simplify a power of a product, for example, (-2xy^3)^5?

• -32x^5y^15

• -10x^5y^15

• -32x^5y^8

• -10x^5y^8

What does a negative exponent indicate in terms of position of the base?

• It remains in the numerator.

• It moves to the denominator.

• It doubles the base.

• It cancels out the base.

If you have a fraction with exponents in the numerator and denominator with the same base, how do you simplify it?

• Add the exponents

• Subtract the exponents

• Multiply the exponents

• Divide the exponents

What is the simplified form of x^0?

• 1

• x

• Undefined

• 0