SOLUTION: 27 to the power x multiply by 9 to the power x+1 all divided by 3 to the power 5x+3

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.

RELATED QUESTIONS
3 to the 1/2 power times 9 to the 1/3 power divided by 27 1/4 power... (answered by Mona27)

3 to the negative 1th power x 7 to 7th power x (3 to the 4th power)3rd power divided by... (answered by Alan3354)

8 to power of 6 divided by 4 to the power of 3 x 2 to the power of... (answered by jsmallt9)

what is 1 x 10 to the second power divided by 1 x 10 to the negative 3... (answered by rfer,Alan3354)

(x to the fifth power divided by x the 6th power) to the 4th... (answered by Alan3354)

x to the 3/2th power =... (answered by RAY100)

4y to the negative 2 power divided by x to the fourth power all times -2... (answered by Alan3354)

9 to the power of X squared plus 2 = 27 to the power of X +... (answered by solver91311)

What is x to the 4th power divided by (x-1)to the 3rd... (answered by jim_thompson5910)