Exponent Rules and Simplification

Miss Smith's math tutorial covers two key rules of exponents: the product rule and the power to power rule. The product rule involves multiplying like bases and adding their exponents, while the power to power rule involves raising a power to another power by multiplying the exponents. The video provides examples and clarifies common misconceptions, such as the importance of recognizing implied exponents of one. The tutorial aims to help students differentiate between these rules and apply them correctly in mathematical problems.

What does the product rule for exponents state?

• Divide the exponents

• Subtract the exponents

• Multiply the exponents

• Add the exponents

If you have x^2 * x^5, what is the result?

• x^10

• x^7

• x^3

• x^5

In the expression 2x^7 * 4x^6, what is the coefficient of the result?

• 12

• 8

• 10

• 6

What is the result of 2x^7 * 4x^6?

• 6x^12

• 8x^12

• 6x^13

• 8x^13

What is the understood exponent if none is written?

• 2

• 1

• 3

• 0

What is the result of x * x^7?

• x^9

• x^6

• x^7

• x^8

What operation is used in the power to power rule?

• Subtraction

• Multiplication

• Division

• Addition

What is the result of (x^2)^5?

• x^15

• x^7

• x^10

• x^25

In the expression (2x^6y^4)^3, what is the exponent of x in the result?

• 24

• 6

• 12

• 18

What is the simplified form of 2^3?

• 6

• 8

• 9

• 12