Final answer:
The expression (x⁷/⁴) / (x¹¹/⁴) simplifies to 1/x by subtracting the exponents and utilizing the rule for negative exponents, which flips the base with a negative exponent to the denominator.
Step-by-step explanation:
To simplify the expression (x⁷/⁴) / (x¹¹/⁴), we apply the rule of Division of Exponentials which states that you subtract the exponents of the exponential terms when dividing like bases. In this case, we subtract the exponent of the denominator from the exponent of the numerator.
The calculation would be as follows:
- x⁷/⁴ ÷ x¹¹/⁴ = x⁷/⁴ - x¹¹/⁴
- This simplifies to x^{(7/4) - (11/4)}
- Subtract the exponents: (7/4) - (11/4) = -4/4 = -1
- So, the expression simplifies to x^{-1}
- Using the property from Eq. A.9 that negative exponents flip the base to the denominator, we have 1/x
Therefore, the simplified expression is 1/x.