Question 838918: 27 to the power x multiply by 9 to the power x+1 all divided by 3 to the power 5x+3
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
|
|
|
