Applying the Rules of Exponents: Basic Examples

This video tutorial covers the fundamental rules of exponents, focusing on multiplying like bases and exponentiation of a power. The instructor explains these concepts using generic examples and then applies them to solve two example problems. The first problem involves multiplying expressions with like bases, while the second problem deals with exponentiation of a power, including negative bases. The video emphasizes common mistakes and provides strategies to avoid them, ensuring a solid understanding of exponent rules.

Why are the rules of exponents important in algebra and calculus?

• They are only used in geometry.

• They help in solving linear equations.

• They are used to find the roots of polynomials.

• They simplify complex expressions involving exponents.

What should you do when multiplying two expressions with the same base?

• Divide the exponents.

• Add the exponents.

• Multiply the exponents.

• Subtract the exponents.

When raising a power to another power, what operation is performed on the exponents?

• Subtract the exponents.

• Multiply the exponents.

• Add the exponents.

• Divide the exponents.

In the expression (2x^3y^4 * 3xy^5)^2, what is the exponent of y after applying the exponent rules?

• 20

• 14

• 10

• 8

What common mistake do people make when dealing with parentheses in exponent expressions?

• Forgetting to add the exponents.

• Applying the exponent only to the variables and not the numbers.

• Dividing the exponents.

• Multiplying the bases instead of the exponents.

What is the simplified form of 2^1 * 3^1 * (2x^3y^4 * 3xy^5)^2?

• 36x^6y^14

• 18x^6y^14

• 36x^5y^14

• 18x^5y^14

In the expression x^5y^7 * (-5x^2y^2)^4, what is the simplified form of the coefficient?

• 5

• 25

• 125

• 625

What is the exponent of x in the simplified form of x^5y^7 * (-5x^2y^2)^4?

• 13

• 5

• 10

• 8

What is the exponent of y in the simplified form of x^5y^7 * (-5x^2y^2)^4?

• 15

• 14

• 8

• 7

What is the final simplified form of x^5y^7 * (-5x^2y^2)^4?

• 625x^13y^14

• 625x^8y^15

• 625x^13y^15

• 625x^8y^14