# Solve for c ((cd)^(4r))/((cd)-r)=c^8d^8

(cd)4r(cd)-r=c8d8
Factor each term.
Remove parentheses.
(cd)4rcd-r=c8d8
Apply the product rule to cd.
c4rd4rcd-r=c8d8
c4rd4rcd-r=c8d8
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
cd-r,1
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of 1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.
1
The factor for cd-r is cd-r itself.
(cd-r)=cd-r
(cd-r) occurs 1 time.
The LCM of cd-r is the result of multiplying all factors the greatest number of times they occur in either term.
cd-r
cd-r
Multiply each term by cd-r and simplify.
Multiply each term in c4rd4rcd-r=c8d8 by cd-r in order to remove all the denominators from the equation.
c4rd4rcd-r⋅(cd-r)=c8d8⋅(cd-r)
Cancel the common factor of cd-r.
Cancel the common factor.
c4rd4rcd-r⋅(cd-r)=c8d8⋅(cd-r)
Rewrite the expression.
c4rd4r=c8d8⋅(cd-r)
c4rd4r=c8d8⋅(cd-r)
Simplify c8d8⋅(cd-r).
Apply the distributive property.
c4rd4r=c8d8(cd)+c8d8(-r)
Multiply c8 by c by adding the exponents.
Move c.
c4rd4r=c⋅c8d8d+c8d8(-r)
Multiply c by c8.
Raise c to the power of 1.
c4rd4r=c1c8d8d+c8d8(-r)
Use the power rule aman=am+n to combine exponents.
c4rd4r=c1+8d8d+c8d8(-r)
c4rd4r=c1+8d8d+c8d8(-r)
c4rd4r=c9d8d+c8d8(-r)
c4rd4r=c9d8d+c8d8(-r)
Rewrite using the commutative property of multiplication.
c4rd4r=c9d8d-(c8d8)r
Multiply d8 by d by adding the exponents.
Move d.
c4rd4r=c9(d⋅d8)-(c8d8)r
Multiply d by d8.
Raise d to the power of 1.
c4rd4r=c9(d1d8)-(c8d8)r
Use the power rule aman=am+n to combine exponents.
c4rd4r=c9d1+8-(c8d8)r
c4rd4r=c9d1+8-(c8d8)r
c4rd4r=c9d9-(c8d8)r
c4rd4r=c9d9-c8d8r
c4rd4r=c9d9-c8d8r
c4rd4r=c9d9-c8d8r
Solve the equation.
Since c is on the right side of the equation, switch the sides so it is on the left side of the equation.
c9d9-c8d8r=c4rd4r
Subtract c4rd4r from both sides of the equation.
c9d9-c8d8r-c4rd4r=0
c9d9-c8d8r-c4rd4r=0
Solve for c ((cd)^(4r))/((cd)-r)=c^8d^8

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