Final answer:
The multiplication of xyz by its reciprocal 1/xyz results in 1 because the xyz in the numerator and denominator cancel each other out, leaving the answer as simply 1.
Step-by-step explanation:
The student's question involves performing the operation xyz * (1/xyz). When you multiply a number or a variable by its reciprocal, the result is 1. This is due to the property of multiplication which states that any number multiplied by its reciprocal equals 1. This concept is similar to working with negative exponents, where raising a number to a negative exponent, you would flip the base to the denominator. However, in this case, you are not dealing with exponents, but rather direct multiplication and division by the same number (or expression).
Therefore, xyz multiplied by (1/xyz) simplifies to 1, because the xyz cancels out with 1/xyz.
Here's the step-by-step explanation:
- Identify the reciprocal relationship between xyz and 1/xyz.
- Multiply xyz by 1/xyz.
- Recognize that xyz divided by xyz equals 1.
- Conclude that the result of the multiplication is 1.