Answer:
[tex]a = 0[/tex]
Step-by-step explanation:
Given
[tex](\frac{1}{7})^{3a+3} = (343)^{a-1}[/tex]
Required
Find a
We start by writing 343 as a factor of 7
[tex](\frac{1}{7})^{3a+3} = (343)^{a-1}[/tex]
[tex](\frac{1}{7})^{3a+3} = (7^3)^{a-1}[/tex]
From laws of indices;
[tex]\frac{1}{a} = a^{-1}[/tex]
So;
[tex](\frac{1}{7})^{3a+3} = (7^3)^{a-1}[/tex] becomes
[tex](7^{-1})^{3a+3} = (7^3)^{a-1}[/tex]
[tex](7)^{(-1){(3a+3)}} = (7)^{3(a-1)}[/tex]
Cancel 7 on both sides
[tex](-1){(3a+3) = {3(a-1)}[/tex]
Open brackets
[tex]-3a - 3 = 3a - 3[/tex]
Collect like terms
[tex]3 - 3 = 3a + 3a[/tex]
[tex]0 = 6a[/tex]
Divide both sides by 6
[tex]0 = a[/tex]
[tex]a = 0[/tex]
