Exploring the Laws of Exponents

In this video, the teacher explains how to simplify algebraic expressions using the power of a power rule. The lesson covers three examples, each demonstrating different aspects of simplification, including handling coefficients, exponents, and negative bases. The teacher provides a step-by-step approach to ensure understanding and concludes with an assignment for further practice.

What is the result of applying the power of a power rule to x^2 when the outside exponent is 3?

• x^5

• x^8

• x^6

• x^9

If y has an exponent of 1 and the outside exponent is 3, what is the new exponent of y?

• 3

• 4

• 2

• 6

How do you simplify 9x^3 squared?

• 81x^9

• 9x^6

• 18x^6

• 81x^6

What is the simplified form of (9x^3)^2?

• 81x^9

• 9x^6

• 81x^6

• 18x^6

What is the result of (-2a^5b^2)^3 for the coefficient -2?

• 2

• -2

• 8

• -8

After applying the exponent rules, what is the new exponent for a in the expression (-2a^5b^2)^3?

• 15

• 10

• 8

• 6

What is the new exponent for b in the expression (-2a^5b^2)^3?

• 6

• 9

• 12

• 3

What is the simplified form of the expression 5x^3y^5 all raised to the power of 2?

• 25x^9y^15

• 10x^6y^10

• 25x^6y^10

• 5x^6y^10

If you have the expression 5x^3y^5 and apply an outside exponent of 2, what is the new exponent for x?

• 5

• 10

• 9

• 6

What is the correct simplification of the coefficient in the expression (5x^3y^5)^2?

• 25

• 10

• 20

• 15