Question

What is the result when the monomial below is raised to the third power?

-5x^3y^2z
a. -125x^6y^4z^3
b. -15x^9y^6z^3
c. -125x^3y^2z^3
d. 15x^3y^2z^3

Answer 1

Raising the monomial -5x^3y^2z to the third power results in -125x^9y^6z^3 by cubing the coefficient and multiplying the exponents of the variables by 3.

Step-by-step explanation:

When we raise a monomial to the third power, we must cube each coefficient and raise each variable to the power of three. In the given monomial -5x^3y^2z, we calculate the cube as follows:

• Cube the coefficient: (-5)^3 = -125
• Raise each variable to the power of 3: (x^3)^3 = x^(3*3) = x^9, (y^2)^3 = y^(2*3) = y^6, and z^3 = z^(1*3) = z^3

Combining these together, the result of raising the given monomial to the third power is -125x^9y^6z^3.