<PRE><B>Question 838918</B>
you have 27^x * 9^(x+1) divided by 3^(5x+3)


27^x is equal to (3*3*3)^x which is equal to (3^3)^x which is equal to 3^3x


9^(x+1) is equal to (3*3)^(x+1) which is equal to (3^2)^(x+1) which is equal to 3^(2*(x+1) which is equal to 3^(2x+2)


3^(5x+3) is ok the way it is.


your equation becomes:


3^3x * 3^(2x+2) divided by 3^(5x+3)


3^3x * 3^(2x+2) is equal to 3^(3x + 2x+2) which is equal to 3^(5x+2)


your equation becomes:


3^(5x+2) divided by 3^(5x+3)


this is equal to 3^((5x+2) - (5x+3)) which is equal to 3^(5x+2-5x-3) which is equal to 3^(-1) which is equal to 1 divided by 3^1) which is equal to 1 divided by 3.


your answer is 1/3.


you can easily check whether this is correct by giving x any value and then replacing x in the original equation by its value and then evaluating the expression.


since x drops out of the equation after simplification, you should always get 1/3 as your answer if we did this correctly.


for example:


your original expression is:


27 to the power x  multiply by 9 to the power x+1 all divided by 3 to the power 5x+3.


replace x with 2.


your original expression becomes:


27 to the power of 2 multiply by 9 to the power of (2+1) all divided by 3 to the power of (5*2 + 3)


this simplifies to:


27 to the power of 2 multiply by 9 to the power of 3 all divided by 3 to the power of 13.


simplifying that further, you get:


729 * 729 all divided by 1594323.


simplifying that further, you get:


531441 divided by 1594323.


since 531441 divides into 1594323 exactly three times, this simplifies to:


1/3.


solution is confirmed as good.



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