Question 1024428
see the following worksheets:


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the graph of the original equation is shown below.


the equation is formed by setting the expression equal to y.


the variable of x was used in place of n for graphing purposes.

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step 1 is the original equation.


step 2 simplifies it by utilizing the fact that (a*(b^c)/d)^e is equal to a^e * (b^c)^e / d^e.


step 3 simplifies it further by utilizing the fact that a^-b = 1/a^b and (a^b)^-c = 1/(a^b)^c.


step 4 simplifies it further by utilizing the fact that (a^b)^c = a^(b*c).


step 5 simplifies it further by utilizing that fact that (a^b)/a^c) = a^(b-c).


step 6 simplifies it further by performing the operation indicated in step 5.


step 7 turns the expression into an equation by setting it equal to 0.


step 8 multiplies both sides of the equation by 2.


step 9 combines like terms.


step 10 utilizes the fact that n^(1/3) is equivalent to (n^1/6)^2.


step 11 factors out the common term of n^(1/6).


step 12 sets the first factor equal to 0 and solves for n to get n = 0.


step 14 sets the second factor equal to 0 and solves for n to get n = 244.140625.


the graph of the original equation confirms the solution is correct.