Final answer:
To simplify radicals, multiply numerators and denominators together while eliminating common factors. In division of exponentials, subtract exponents after dividing digit terms. Ensure the final simplified form is checked for reasonableness.
Step-by-step explanation:
To simplify radicals, you should eliminate terms wherever possible. For instance, when multiplying radicals, you multiply the numerators together and the denominators together. Simplification involves reducing any common factors. If you encounter a power inside a radical, like √x², recall that this is equivalent to the principal root, which simplifies to x because x times x equals x². Similarly, for exponential expressions like 5¹, where adding the exponent to 1 gives a square root of 5.
Division of exponentials follows a different rule. Here, you divide the digit term of the numerator by the digit term of the denominator and subtract the exponents of the exponential terms.
Remember to use a simplified subscript in the final formula. If the subscript is one, it should not be written. Always check your final answer to ensure it is reasonable. For the multiplication of fractions, symbolically, we follow the intuition that you multiply numerators by numerators and denominators by denominators, simplifying by common factors as needed.
For ionic compounds, transpose only the number of the positive charge to become the subscript of the anion, and the number of the negative charge to become the subscript of the cation, reducing to the lowest ratio possible. This ensures the formula is empirically correct and reflects a proper balance of charges.