Final answer:
The multiplication of exponents with the same base results in adding the exponents, whereas dividing them results in subtracting the exponents. Therefore, x^4 * x^3 is greater than x^4 / x^3, because x^7 is typically greater than x.
Step-by-step explanation:
The question involves understanding the rules of exponents for multiplication and division. When you multiply two exponents with the same base, you add the exponents (x^4 * x^3 = x^(4+3) = x^7). However, when you divide exponents with the same base, you subtract the exponents (x^4 / x^3 = x^(4-3) = x^1 = x). Therefore, the result of x to the power of 4 times x to the power of 3 is x raised to the 7th power, whereas x to the power of 4 divided by x to the power of 3 is simply x.
Since x^7 represents x multiplied by itself seven times, it will generally be greater than x itself, unless x is 1 or 0. Thus, the correct answer to how x^4 * x^3 differs from x^4 / x^3 is: b) x^4 * x^3 is greater than x^4 / x^3.