Final answer:
To simplify (c^8d^5)/(cd) using the quotient rule for exponentials, we subtract the exponents of like bases, resulting in the simplified form c^7d^4.
Step-by-step explanation:
To use the quotient rule for exponentials, we need to divide the digit term of the numerator by the digit term of the denominator and subtract the exponents of the exponential terms when we have a division of similar bases. In the given expression (c⁸d⁵)/(cd), we divide the terms with the same base and subtract their exponents.
The expression simplifies as follows:
- For the base c, we subtract the exponent in the denominator from the exponent in the numerator: c⁸ divided by c is c⁷ (8 - 1 = 7).
- For the base d, we perform a similar operation: d⁵ divided by d is d⁴ (5 - 1 = 4).
Therefore, the simplified form of the expression is c⁷d⁴.