Question

Which statements are true? Check all that apply.

A) David correctly simplified the power of products in his first step by adding exponents.
B) Audrey first applied division of like bases by subtracting the exponents.
C) Next, David will apply the quotient of powers.
D) David’s work is incorrect.
E) Audrey’s work is correct.
F) The correct simplified final answer is x²⁴/64y¹⁵

Answer 1

The correct statements are: David correctly simplified the power of products in his first step by adding exponents, Audrey’s work is correct, and the correct simplified final answer is x²⁴/64y¹⁵.

Step-by-step explanation:

The correct statements are:

• David correctly simplified the power of products in his first step by adding exponents
• Audrey’s work is correct
• The correct simplified final answer is x²⁴/64y¹⁵

Here is a step-by-step explanation of each statement:

• Statement A is true because when we multiply two exponentiated pieces together, we add the exponents. For example, (x^a)(x^b) = x^(a + b).
• Statement B is false because when we divide exponentiated terms with the same base, we subtract the exponents. For example, (x^a)/(x^b) = x^(a - b).
• Statement C is false because at this point, David will apply the power of a quotient rule, where we subtract the exponents. For example, (x^a)/(y^b) = x^(a - b)/y^(1).
• Statement D is false because David's work is correct.
• Statement E is true because Audrey's work is correct.
• Statement F is true because the correct simplified final answer is x²⁴/64y¹⁵.