Final answer:
The monomial (1/3 x⁵)³ ∙ 81x⁴ simplifies to 3x¹⁹ in standard form after applying the order of operations.
Step-by-step explanation:
The question involves simplifying and writing a monomial in standard form. We apply the Order of Operations (usually remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Let's start with the operation: (1/3 x⁵)³ ∙ 81x⁴
First, let's deal with the cube operation. (1/3)³ = 1/27 and (x⁵)³ = x¹⁵, so (1/3 x⁵)³ = 1/27x¹⁵
Then we multiply this by 81x⁴. So, 1/27 x¹⁵ ∙ 81x⁴ = 3x¹⁹, because 1/27*81 = 3 and when we multiply variables with the same base, we add the exponents: 15 + 4 = 19.
So, the monomial in standard form is 3x¹⁹.
Learn more about Order of Operations