# Solve for y cube root of (x^3)/(cy^4)=x/(4y( cube root of y))

To remove the radical on the left side of the equation, cube both sides of the equation.
Simplify each side of the equation.
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify.
Multiply by .
Combine and simplify the denominator.
Multiply and .
Move .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify.
Multiply by by adding the exponents.
Move .
Multiply by .
Rewrite as .
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Apply the product rule to .
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Simplify the denominator.
Raise to the power of .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Solve for .
Set up the rational expression with the same denominator over the entire equation.
Multiply each term by a factor of that will equate all the denominators. In this case, all terms need a denominator of . The expression needs to be multiplied by to make the denominator . The expression needs to be multiplied by to make the denominator .
Multiply the expression by a factor of to create the least common denominator (LCD) of .
Move to the left of .
Multiply the expression by a factor of to create the least common denominator (LCD) of .
Multiply by .
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
Subtract from both sides of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
Rewrite as .
Pull terms out from under the radical, assuming real numbers.
Solve for y cube root of (x^3)/(cy^4)=x/(4y( cube root of y))

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