Question

Two students have partially simplified the same expression. audrey’s work: ( x3y−2 22x−5y3 ) 3 = ( x8y−5 22 ) 3 = x24y−15 26 david’s work: ( x3y−2 22x−5y3 ) 3 = x9y−6 26x−15y9 which statements are true? check all that apply. david correctly simplified the power of products in his first step by adding exponents. audrey first applied division of like bases by subtracting the exponents. next david will apply the quotient of powers. david’s work is incorrect. audrey’s work is correct. the correct simplified final answer isstartfraction x superscript 24 baseline over 64 y superscript 15 baseline endfraction

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 the 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

To determine which statements are true, let's analyze Audrey and David's work step by step. From the analysis, David correctly simplified the power of products in his first step by adding exponents, but his work is incorrect. Audrey's work is correct, and the correct simplified final answer is x^24/64y^15.

Step-by-step explanation:

To determine which statements are true, let's analyze Audrey and David's work step by step:

Audrey's work: (x3y-2)(22x-5y3)3 = (x8y-5)(22)3 = x24y-1526

David's work: (x3y-2)(22x-5y3)3 = x9y-626x-15y9

From the analysis, the following statements are true:

A) David correctly simplified the power of products in his first step by adding exponents.

D) David's work is incorrect.

E) Audrey's work is correct.

F) The correct simplified final answer is x24/64y15.