Question

For what value of a does (1/7) ^3a+3 = 343^a-1?

Answer 1

Answer: 0

Step-by-step explanation:

Answer 2

Wheee

ok, remember that when
x^a=x^b, when x=x, then a=b

also
x^-m=1/(x^m)
and
(x^m)^n=x^(mn)
so

$(\frac{1}{7})^{3a+3}=343^{a-1}$
we can rewrite 1/7 as 7^-1
so
$(7^{-1})^{3a+3}=343^{a-1}$
$(7)^{(-1)(3a+3)}=343^{a-1}$
$(7)^{-3a-3}=343^{a-1}$
and 343=7^3
$(7)^{-3a-3}=(7^3)^{a-1}$
$(7)^{-3a-3}=7^{(3)(a-1)}$
$(7)^{-3a-3}=7^{3a-3}$
7=7 so
-3a-3=3a-3
add 3a to both sides
-3=6a-3
add 3 to both sides
0=6a
0=a

a=0