Final answer:
To express y^12 as the cube of a monomial, we find a monomial whose exponent, when multiplied by 3, equals 12. The term y^4, when cubed, becomes (y^4)^3, which simplifies to y^12.
Step-by-step explanation:
Writing the term y^12 as the cube of a monomial involves finding a monomial that, when cubed, gives us y^12. Cubing a monomial means we will cube the coefficient (if there is one) and multiply the exponent by 3. To write y^12 as a cube, we need to find an exponent that when multiplied by 3 gives us 12. The necessary exponent for y would be 4 since 4 multiplied by 3 is 12. Therefore, the cube of the monomial y^4 gives us the term y^12.
When dealing with cubing of exponentials, remember that only the exponent is affected by the operation when the base is a variable. No coefficients are involved in this particular example. In other instances, if you have a numeric coefficient, you would cube that number as well, following the usual rules of exponents.
Thus, the original term y^12 can be expressed as (y^4)^3. This is because when we apply the exponent rule of powers raised to powers, we multiply the exponents, resulting in y^(4*3), which simplifies to y^12.