Exploring the Product Rule of Exponents

This video tutorial introduces the properties of exponents, focusing on the product rule. It explains how to multiply terms with the same base by adding their exponents. The tutorial provides several examples, including basic applications, scenarios with multiple variables, and more complex cases involving multiple terms. The video concludes with an advanced example that hints at other exponent properties to be covered in future videos.

What does X to the third power expand to?

• X + X + X

• X * X * X

• X ^ 3

• 3 * X

What does the expression X^3 * X^2 simplify to?

• X^5

• 5X

• X^6

• X^10

How do you simplify X^a * X^b?

• X^(a - b)

• X^(a / b)

• X^(a * b)

• X^(a + b)

What is the result of multiplying 3x^5 by -2x^7?

• -6x^12

• 6x^12

• -5x^12

• -6x^35

If you multiply 3x^5 by -2x^7, what do you multiply together first?

• 3 and 5

• The coefficients 3 and -2

• The exponents 5 and 7

• x^5 and x^7

When combining 2a^2 * 5a^4, what is the exponent of 'a' in the result?

• a^6

• 10a^6

• a^8

• 2a^6

In the expression 2a^2 * 5a^4, what is the coefficient of 'a' in the result?

• 2

• 5

• 7

• 10

What is the total number of X's in the expression X^3 * X^2 * X^4?

• X^9

• 9X

• X^8

• X^6

What is the simplified form of (2x^4)^3 using the product rule?

• 8x^7

• 6x^12

• 8x^12

• 8x^11

What does the exponent '3' signify in the expression (2x^4)^3?

• None of the above

• Add three to the exponent of x

• Divide the expression inside the parenthesis by three

• Multiply the expression inside the parenthesis three times