Simplification of an expression is making it as simple as possible. The simplified form of the considered expression is given by: Option D: [tex]72a^3[/tex]
What are some basic properties of exponentiation?
If we have [tex]a^b[/tex] then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\ a^b \times a^c = a^{b+c}\\\\^n\sqrt{a} = a^{1/n}\\(ab)^c = a^c \times b^c[/tex]
For the given case, the expression is simplified by using the given rules as:
[tex][3(2a)^{3/2}]^2 = 3^2 \times (2a)^{\dfrac{3}{2} \times 2} = 9 \times (2a)^3\\[/tex]
[tex][3(2a)^{3/2}]^2 = 9 \times 8 \times a^3 = 72a^3[/tex]
Thus, the simplified form of the considered expression is given by: Option D: [tex]72a^3[/tex]
Learn more about exponent here:
https://brainly.com/question/26676307
