To determine which polynomial is written in standard form, we need to recall that a polynomial in standard form is arranged in descending order of the degrees of the terms.
Given the polynomial \(8x^2y^2-3x^3y+4x^4-7xy^3\), we need to rearrange the terms in descending order based on the total degree of each term.
1. The term \(4x^4\) has the degree of 4 (since the exponent of \(x\) is 4).
2. The term \(-3x^3y\) has the degree of 4 (since the sum of the exponents \(3+1=4\)).
3. The term \(8x^2y^2\) also has the degree of 4 (since the sum of the exponents \(2+2=4\)).
4. The term \(-7xy^3\) has the degree of 4 (since the sum of the exponents \(1+3=4\)).
Next, we list these terms in descending order:
1. \(4x^4\)
2. \(-3x^3y\)
3. \(8x^2y^2\)
4. \(-7xy^3\)
Thus, the polynomial in standard form is: \(4x^4 - 3x^3y + 8x^2y^2 - 7xy^3\).
Therefore, the polynomial written in standard form is:
[tex]\[ \boxed{4 x^4 - 3 x^3 y + 8 x^2 y^2 - 7 x y^3} \][/tex]
