Understanding Properties of Exponents

This video tutorial from MooMooMath and Science covers the properties of exponents, focusing on the power of a product rule. It provides examples of how to apply this rule, including handling negative exponents and complex scenarios. The tutorial also highlights common mistakes to avoid when working with exponents.

What is the power of a product rule in exponents?

• (ab)^m = a^m + b^m

• a^m / b^m = (a/b)^m

• a^m * b^m = (ab)^m

• (ab)^m = a^m * b^m

If (4a^2b^3)^5 is expanded, what is the exponent of 'a'?

• 15

• 10

• 5

• 20

In the expression (x^4y^7)^3, what is the resulting exponent of 'y'?

• 21

• 14

• 7

• 28

How is 4^(-1) expressed in a simplified form?

• 4^1

• 4

• -4

• 1/4

What is the simplified form of (2x^2y^(-2))^2?

• 4x^4/y^4

• 4x^4y^4

• x^4/y^4

• x^4y^4

What is the result of (3k^4)^4?

• 81k^4

• 81k^16

• 3^4k^4

• 3k^16

How is (x^4/y^(-4)) simplified?

• x^4y^(-4)

• x^4/y^4

• x^4y^4

• y^4/x^4

Which of the following is NOT a correct application of the power of a product rule?

• (a/b)^m = a^m / b^m

• (ab)^m = a^m + b^m

• (a^m)^n = a^(mn)

• (ab)^m = a^m * b^m

What is the correct approach to expand (3x^2 + y)^3?

• Use the power of a product rule

• Use the associative property

• Use the FOIL method

• Use the distributive property

Why does the power of a product rule not apply to (3x^2 + y)^3?

• Because it involves multiplication

• Because it involves addition

• Because it involves subtraction

• Because it involves division