Understanding Exponents and Their Properties

The video tutorial reviews key vocabulary such as base, exponent, and monomial, and explains various properties of exponents including power of one, power of zero, negative exponents, product of powers, quotient of powers, and power of powers. It then applies these properties to simplify mathematical expressions through examples.

What is the term for a number or variable that is multiplied by itself repeatedly?

• Exponent

• Base

• Monomial

• Coefficient

What is the result of any number raised to the power of zero?

• One

• Negative one

• The number itself

• Zero

How do you simplify an expression with a negative exponent?

• Add the exponent

• Multiply by zero

• Take the reciprocal and make the exponent positive

• Subtract the exponent

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

• Subtract them

• Add them

• Divide them

• Multiply them

What is the result of dividing x^2 by x^5?

• x^3

• x^7

• x^-3

• x^10

What happens to the exponents when a power is raised to another power?

• They are multiplied

• They are added

• They remain unchanged

• They are subtracted

In the expression (2x^3)^5, what is the exponent of x after applying the power of powers rule?

• 5

• 3

• 8

• 15

What is the simplified form of 4x^2 * x * y^3 * y^3?

• 4x^3y^6

• 4x^2y^3

• 4x^3y^9

• 4x^5y^9

How do you simplify the expression (x^1)/(x^-2)?

• x^1

• x^-3

• x^3

• x^2

What is the simplified form of the expression 81y^8/x^4?

• 81x^4/y^8

• 81y^8/x^4

• x^4/81y^8

• y^8/81x^4