If the cube root of y is 3 then cube root of y³ =

Rationale

Cube root of y^3 is 27.

Given that the cube root of y equals 3, we can express y as 3^3. Therefore, when calculating the cube root of y^3, we replace y with 3^3, leading us to (3^3)^(3/3), which simplifies to 3^3 or 27.

A (3^2) YOUR ANSWER

This option represents 9, which is incorrect. The expression 3^2 does not correspond to the cube root of y^3 since y^3 simplifies to 3^9, and its cube root must yield a value greater than 9.

B (3^3) YOUR ANSWER

While this option equals 27, it is not the result we seek for the cube root of y^3 in this context. The cube root of y^3 simplifies further, which gives us a different exponent than 3.

C (3^6) YOUR ANSWER

This choice is 729, which is incorrect. The cube root of y^3 is not equal to 3^6, as it does not align with the calculations derived from the value of y being 3^3.

D (3⁹) CORRECT

This is the correct option. When y is expressed as 3^3, y^3 equals 3^(3*3), which simplifies to 3^9. The cube root of 3^9 simplifies to 3^(9/3), resulting in 3^3 or 27.

E (3^18) YOUR ANSWER

This option equals 387420489, which is incorrect. The result of the cube root of y^3 is not this value, as y^3 is only 3^9, not 3^18.

Conclusion

In summary, the cube root of y^3 simplifies to 3^3 or 27, given that y is defined as 3^3. The other choices reflect incorrect calculations or misinterpretations of the expression, emphasizing the importance of accurately applying the properties of exponents in cube roots.

If the cube root of y is 3 then cube root of y³ =

Cube root of y^3 is 27.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test