Final answer:
To simplify the expression v^1/2 * v^-19/10, subtract the exponents to get v to the power of negative four-fifths (v^-4/5). This process is part of simplifying expressions involving the same base with exponents.
Step-by-step explanation:
The question involves simplifying mathematical expressions with exponents. To simplify the given expression v¹⁄² * v⁻¹⁹⁄¹⁰, we use the property of exponents that allows us to subtract exponents when multiplying two powers of the same base. Thus, we combine the exponents by adding the exponents of v (1/2 and -19/10). The simplified expression is v⁻⁴⁄µ (v to the power of negative four-fifths).
To check if the answer is reasonable, we consider that subtracting a larger negative fraction from a smaller positive fraction should result in a negative fraction, which aligns with our solution.