Correct Answer:
A. x⁴
Correct Answer: 1
To simplify the expression x(x²)/x³, first multiply the terms in the numerator. Since x × x² = x³, the expression becomes x³/x³. According to the laws of exponents, when two powers with the same base are divided, their exponents are subtracted: x³ ÷ x³ = x³⁻³ = x⁰. Any non-zero number raised to the power of zero is equal to 1. Therefore, the simplified value of the expression is 1. Questions based on exponent rules are frequently asked in competitive examinations because they test understanding of the basic laws of algebra. Students should remember that x⁰ = 1 only when x is not equal to zero.
- Numerator: x × x² = x³.
- Exponent Rule: x³/x³ = x⁰.
- Identity: x⁰ = 1 (for x ≠ 0).
- Topic: Laws of Exponents.
- Correct Answer: 1.