Question

!! Solve for the following equation step by step and justify your steps when using an exponential property.

(7^(x))^(4)=(7^(2)*7^(3))/(7^(3x))

Answer 1

x = 5/7

Explanation:

Here, we want to get the value of x

Firstly, according to indices;

(a^m)^n = a^(m * n) = a^mn

Also;

a^m * a*n = a^(m + n)

a^0 = 1 (any number raised to zero as its power is 1)

And lastly;

a^m divided by a^n = a^(m-n)

So using these we can have;

7^4x = 7^( 2 + 3)/7^3x

7^4x = 7^5/7^3x

7^4x = 7^(5-3x)

Since we have the same bases, we have to equate the powers

4x = 5-3x

4x + 3x = 5

7x = 5

x = 5/7