Simplify x^4 / x^7.

Simplify x^4 / x^7.

• A. x^0
• B. x^3
• C. x^7
• D. x^-3

Answer: (D)

When you divide expressions with the same base, subtract the exponents: x^4 / x^7 = x^(4−7) = x^-3. A negative exponent means the reciprocal, so x^-3 is the same as 1/x^3. This is the correct simplification. The other forms would come from using different exponent operations (for example, x^0 would imply the exponents were equal or cancel in a way that leaves 1, which isn’t the case here, and x^3 would come from adding or reversing the subtraction).

When you divide expressions with the same base, subtract the exponents: x^4 / x^7 = x^(4−7) = x^-3. A negative exponent means the reciprocal, so x^-3 is the same as 1/x^3. This is the correct simplification. The other forms would come from using different exponent operations (for example, x^0 would imply the exponents were equal or cancel in a way that leaves 1, which isn’t the case here, and x^3 would come from adding or reversing the subtraction).