The given monomial in standard form is [tex]16a^6x^4y^2[/tex]
Solution:
A Monomial in standard form is the product of one or more factors: a constant coefficient and one factor for each variable in the expression.
Given monomial is:
[tex](-4x^2ya^3)^2[/tex]
We use the following law of exponents to solve the above monomial:
[tex](ab)^n = a^nb^n\\\\(a^n)^m = a^{mn}[/tex]
Using these in given monomial, we get
[tex](-4x^2ya^3)^2 = (-4)^2(x^2)^2(y)^2(a^3)^2[/tex]
Now applying the law of exponent [tex](a^n)^m = a^{mn}[/tex] we get,
[tex](-4)^2(x^2)^2(y)^2(a^3)^2 = 16x^{2 \times 2}y^2a^{3 \times 2} = 16x^4y^2a^6[/tex]
A monomial is in standard form when its term of highest degree is first, its term of 2nd highest is 2nd etc
Writing in standard form we get,
[tex]\rightarrow 16a^6x^4y^2[/tex]
Thus the given monomial is written in standard form
