Question

For what value of a does (one-seventh) Superscript 3 a + 3 Baseline = 343 Superscript a minus 1?

Answer 1

a=0 is correct!!!!!

Explanation:

jus got 100% on edge!!

Answer 2

`a = 0`

Explanation:

Given

`((1)/(7))^(3a+3) = (343)^(a-1)`

Required

Find a

We start by writing 343 as a factor of 7

`((1)/(7))^(3a+3) = (343)^(a-1)`

`((1)/(7))^(3a+3) = (7^3)^(a-1)`

From laws of indices;

`(1)/(a) = a^(-1)`

So;

`((1)/(7))^(3a+3) = (7^3)^(a-1)` becomes

`(7^(-1))^(3a+3) = (7^3)^(a-1)`

`(7)^{(-1){(3a+3)}} = (7)^(3(a-1))`

Cancel 7 on both sides

`(-1){(3a+3) = {3(a-1)}`

Open brackets

`-3a - 3 = 3a - 3`

Collect like terms

`3 - 3 = 3a + 3a`

`0 = 6a`

Divide both sides by 6

`0 = a`

`a = 0`