Which of the following has the highest degree?

1. $x^5 + 2x^5$

2. $2^8$

3. $-\dfrac{3a^3b^2c}{4}$

4. $\dfrac{7a^6b^5}{-5a^3b^4}$

The highest degree of a polynomial is the greatest sum of the exponents of the variables found in any single term of that expression.

Analysis:

1. $x^5 + 2x^5 = 3x^5$ → Degree = 5

2. $2^8$ → Constant, Degree = 0

3. $a^3b^2c$ → Degree = 3 + 2 + 1 = 6

4. $\dfrac{a^6b^5}{a^3b^4} = a^3b^1$ → Degree = 3 + 1 = 4

Among these, $-\dfrac{3a^3b^2c}{4}$ has the highest degree i.e., 6.

Hence, option 3 is the correct option.