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

Answer 1

Audrey correctly simplifies the expression while David makes an error in exponent simplification.

Step-by-step explanation:

In this question, the students Audrey and David have partially simplified the same expression, ( x^3y^-2 / 22x^-5y^3 )^3. Audrey's work simplifies to x^24y^-15 / 26, while David's work simplifies to x^9y^-6 / 26x^-15y^9. Let's break down the steps taken by each student:

Audrey: She correctly raised both the numerator and denominator to the power of 3, resulting in x^9y^-6 / 66x^-15y^9. Then, she simplified the powers by multiplying them together, giving x^24y^-15 / 26.

David: He also correctly raised both the numerator and denominator to the power of 3, resulting in x^9y^-6 / 66x^-15y^9. However, he made an error when simplifying the powers. Instead of adding them together, he only added the exponents of x and y separately, resulting in x^9y^-6 / 26x^-15y^9.

Therefore, Audrey's work is correct while David's work has an error in the exponent simplification.

Answer 2

-Aubrey first applied division of like bases by subtracting the exponents.

-Next David will apply the quotient of powers.

-Aubrey's work is correct .

-The correct simplified answer is x^24/64y^15