Question 177651
your equation is:
{{{((6*x^5*y^3*z)*3*x^2)/(2*x*y^2*z^5)}}}
if you remove the parentheses from the numerator, this becomes:
{{{(6*x^5*y^3*z*3*x^2)/(2*x*y^2*z^5)}}}
since a*b is the same as b*a, you can move the variables around until you get similar variables together which makes your equation the same as:
{{{(6*3*x^5*x^2*y^3*z)/(2*x*y^2*z^5)}}}
since {{{x^5 * x^2 = x^(5+2) = x^7}}}, your equation becomes:
{{{(6*3*x^7*y^3*z)/(2*x*y^2*z^5)}}}
since {{{x^7 / x = x^7 / x^1 = x^(7-1) = x^6}}}, your equation becomes:
{{{(6*3*x^6*y^3*z)/(2*y^2*z^5)}}}
since {{{y^3 / y^2 = y^(3-2) = y^1 = y}}}, your equation becomes:
{{{(6*3*x^6*y*z)/(2*z^5)}}}
since {{{z / z^5 = z^1 / z^5 = z^(1-5) = z^(-4) = 1/z^4}}}, your equation becomes:
{{{(6*3*x^6*y)/(2*z^4)}}}
since {{{(6*3)/2 = 3*3 = 9}}}, your equation becomes:
{{{(9*x^6*y)/(z^4)}}}
since you can't simplify any further, this will be your final equation.
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to prove your answer is correct, substitute values for x, y, and z in your original equation and in your final equation to see that the answer comes out the same.
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let:
x = 2
y = 3
z = 4
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your final equation is:
{{{(9*x^6*y)/(z^4)}}}
substituting, we get:
{{{(9*2^6*3)/(4^4)}}}
which becomes:
{{{(9*64*3)/(256)}}}
which becomes:
{{{(1728)/(256)}}}
which becomes:
6.75
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your original equation is:
{{{(6*x^5*y^3*z*3*x^2)/(2*x*y^2*z^5)}}} after removing the parentheses.
substituting, we get:
{{{(6*2^5*3^3*4*3*2^2)/(2*2*3^2*4^5)}}}
which becomes:
{{{(6*32*27*4*3*4)/(2*2*9*1024)}}}
which becomes:
{{{(248832)/(36864)}}}
which becomes:
6.75
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since the original equation = 6.75 and the final equation = 6.75, then the original equation equals the final equation and we are good.
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your answer is:
{{{((6*x^5*y^3*z)*3*x^2)/(2*x*y^2*z^5)}}} = {{{(9*x^6*y)/(z^4)}}}