Final answer:
To simplify the given exponential expressions, utilize the exponent rules for multiplication (add exponents), power of a power (multiply exponents), and division (subtract exponents) to get x^7, x^20, and x^6 respectively.
Step-by-step explanation:
The student has asked to simplify several exponential expressions. When simplifying expressions with exponents, one must remember the rules of exponents for multiplication, power of a power, and division.
To simplify x^3 * x^4, we add the exponents since the bases are the same. Therefore, we get x^(3+4) = x^7.
The expression (x^4)^5 represents a power of a power, which means we multiply the exponents. This simplifies to x^(4*5) = x^20.
For the expression (x^8) / (x^2), we subtract the exponent of the denominator from the exponent of the numerator since the bases are again the same. The result is x^(8-2) = x^6.