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

Question

Eva Abramson · Accepted Answer

See a solution process below:

We can rewrite the expression using this rule for dividing fractions: #(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))# #c^5/2 -: c^3/(cd^2) => (color(red)(c^5)/color(blue)(2))/(color(green)(c^3)/color(purple)(6d^2)) => (color(red)(c^5) xx color(purple)(6d^2))/(color(blue)(2) xx color(green)(c^3)) => (cancel(color(red)(c^5))c^2 xx color(black)(cancel(color(purple)(color(purple)(6)))3d^2))/(cancel(color(blue)(2)) xx cancel(color(green)(c^3))) =># #3c^2d^2#

Isaiah Anthony · Answer

undefined 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.