SOLUTION: Solve for the following equation step by step and justify the steps when using an exponential property. (7^(x))^(4) = (7^(2 )* 7^(3))/(7^(3x))

Question 1053329: Solve for the following equation step by step and justify the steps when using an exponential property.
(7^(x))^(4) = (7^(2 )* 7^(3))/(7^(3x))

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
(7^x)^4 is equal to 7^(4x).

7^2 * 7^3 is equal to 7^(2+3) which is equal to 7^5.

7^5 / 7^(3x) is equal to 7^(5 - 3x).

you wind up with 7^(4x) is equal to 7^(5 - 3x)

this is true if and only if 4x = 5 - 3x.

solve for x to get x = 5/7.

that's your answer.

here's a lesson on the properties of exponents that you might find helpful.

http://www.mathplanet.com/education/algebra-1/exponents-and-exponential-functions/properties-of-exponents

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