Question

10x⁵ y⁵ z⁵ * 12x⁴ y⁴ z² * 8x² y⁸ z * 6x² y⁴ z

Answer 1

To solve the multiplication of polynomials with exponents, the student should multiply the coefficients and add the exponents of like variables, resulting in the expression 5760x^13y^21z^9.

Step-by-step explanation:

The student's question involves multiplying polynomial expressions with exponents. To multiply these expressions, we need to apply the rule that when we multiply terms with the same base, we add their exponents. Here, we will multiply coefficients and add the exponents of like variables (x, y, and z).

Let's multiply the coefficients first:

• 10 * 12 * 8 * 6 = 5760

Now, for the variables:

• x to the power of (5 + 4 + 2 + 2) = x13
• y to the power of (5 + 4 + 8 + 4) = y21
• z to the power of (5 + 2 + 1 + 1) = z9

The final simplified expression is 5760x13y21z9.