To simplify the expression x(x²)/x³, first multiply the terms in the numerator. Using the law of exponents, x × x² = x³. The expression therefore becomes x³/x³. According to the exponent rule am/an = am−n (where a ≠ 0), we subtract the exponents: x3−3 = x⁰. Since any non-zero number raised to the power of zero equals 1, the simplified value of the expression is 1.
Exponent laws are fundamental in algebra and are widely used to simplify mathematical expressions. Some important rules include: am × an = am+n, am/an = am−n, and a⁰ = 1 for a ≠ 0. These principles are frequently tested in school mathematics as well as competitive examinations because they provide a quick and systematic method for solving algebraic problems involving powers and exponents.
Why the other options are incorrect:
- x⁴ is incorrect because the exponents are not added after dividing; the numerator first becomes x³, which then cancels with the denominator.
- x⁶ is incorrect because it results from incorrectly multiplying all exponents instead of applying the laws of exponents.
- x⁷ is incorrect because there is no valid exponent rule that produces x⁷ from the expression x(x²)/x³.