10
QuizMultiple Choice

Solving Systems of Equations in Three Variables — Unit test

Question 10 • Crowley Summer 26 Credit Recovery Algebra 2 A

Miguel stated that any monomial can be a cube root. Sylvia disagreed and said that a monomial cube root must have exponents divisible by 3. Who is correct, and why?

Answer
A
Sylvia is correct. Any variable term, when it is cubed, always has an exponent divisible by 3.
B
Miguel is correct. Any monomial can be a perfect cube root because, when it is cubed, the variables will have exponents divisible by 3.
C
Sylvia is correct. In order for the cube to have exponents that are divisible by 3, the cube root has to be divisible by 3.
D
Miguel is correct. Sylvia confused the perfect square root with the perfect cube root.

Explanation

Miguel is correct: a monomial can be the cube root of its own cube. For example, cubing 2x²y gives 8x⁶y³, whose variable exponents are divisible by 3. The exponents in the cube are multiplied by 3; the exponents in the cube root do not need to be divisible by 3. So the choice saying any monomial can be a perfect cube root is correct.

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