Question

Write the monomial in its standard form and name its coefficient:
1/4 b²a * 16a⁴

Answer 1

The monomial 1/4 b²a * 16a⁴ in standard form is 4a⁵b², with the coefficient being 4.

Step-by-step explanation:

To write the monomial 1/4 b²a * 16a⁴ in its standard form, we must first multiply the numerical coefficients and then apply the laws of exponents to combine the like bases. The numerical coefficients are 1/4 and 16. Multiplying these together, we get 1/4 * 16 = 4. Next, we combine the like bases by adding their exponents, which gives us b² and a¹ * a⁴, resulting in a⁵ since a¹ * a⁴ = a¹+⁴. Therefore, the standard form of the monomial is 4a⁵b². The coefficient of this monomial is 4.