Final answer:
To remove a radical in the denominator, use the process of rationalization by multiplying the numerator and denominator by a value that cancels out the radical. In dimensional analysis, use a conversion factor with the undesired unit in the numerator to cancel it out. For exponential terms, subtract the exponents when the same base appears in both the numerator and denominator.
Step-by-step explanation:
When you encounter a radical in the denominator of an expression, you will typically use a process called rationalization to eliminate it. Rationalization involves multiplying the numerator and the denominator by a value that will remove the radical when distributed. This could mean using the conjugate in cases of binomial denominators. For simple cases with a monomial radical in the denominator, you multiply by the same radical present in the denominator to effectively cancel it out.
If you are dealing with dimensional analysis and want to convert units, and the unit you need to eliminate is in the denominator, employ a conversion factor where that unit is in the numerator. This cancels out the original unit when you multiply across. This is a fundamental approach in physics and chemistry for converting units and solving equations involving derived units.
The process of division of exponentials is another context where managing denominators is crucial. To divide terms with the same base raised to exponents, you simply subtract the exponent in the denominator from the exponent in the numerator. If numeric coefficients are present, those will be divided normally.