# How do you find the quotient of #c^5/2divc^3/(6d^2)#?

See a solution process below:

We can rewrite the expression using this rule for dividing fractions:

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To find the quotient of c^5/2 divided by c^3/(6d^2), we can simplify the expression by applying the rules of exponents.

First, we can simplify c^5/2 by raising c to the power of 5/2, which is equivalent to taking the square root of c^5. This gives us √(c^5) = c^(5/2).

Next, we can simplify c^3/(6d^2) by dividing c^3 by 6d^2. This gives us c^3 / (6d^2).

To divide c^(5/2) by c^3 / (6d^2), we can multiply c^(5/2) by the reciprocal of c^3 / (6d^2), which is (6d^2) / c^3.

Multiplying c^(5/2) by (6d^2) / c^3, we get (c^(5/2)) * ((6d^2) / c^3).

Simplifying further, we can cancel out one c term from the numerator and denominator, resulting in (6d^2) * (c^(5/2 - 3)).

Finally, we can simplify the exponent by subtracting 3/2 from 5/2, which gives us (6d^2) * (c^(2/2)).

Simplifying c^(2/2) to c^1, we have (6d^2) * c.

Therefore, the quotient of c^5/2 divided by c^3/(6d^2) is (6d^2) * c.

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