Respuesta :

apologiabiology
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

[tex](\frac{1}{7})^{3a+3}=343^{a-1}[/tex]
we can rewrite 1/7 as 7^-1
so
[tex](7^{-1})^{3a+3}=343^{a-1}[/tex]
[tex](7)^{(-1)(3a+3)}=343^{a-1}[/tex]
[tex](7)^{-3a-3}=343^{a-1}[/tex]
and 343=7^3
[tex](7)^{-3a-3}=(7^3)^{a-1}[/tex]
[tex](7)^{-3a-3}=7^{(3)(a-1)}[/tex]
[tex](7)^{-3a-3}=7^{3a-3}[/tex]
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

The value of [tex]a[/tex] will be [tex]0[/tex] .

What are exponent ?

Exponent is a number or letter written above and to the right of a mathematical expression called the base.

We have,

[tex](\frac{1}{7})^{3a+3} = (343)^{a-1}[/tex]

Now,

Using the exponent rule;

[tex](\frac{1}{n}) ^a=n^{(-a)}[/tex]

So,

Rewrite the given expression;

[tex](\frac{1}{7})^{3a+3} = (343)^{a-1}[/tex]

[tex](7)^{-(3a+3)} = (7^3)^{a-1}[/tex]

[tex](7)^{-3a-3} = (7)^{3a-3}[/tex]

Now,

Using Distributive property;

i.e. comparing the powers;

[tex]-3a-3=3a-3[/tex]

⇒[tex]-3a-3a=3-3[/tex]

[tex]-6a=0[/tex]

[tex]a=0[/tex]

So, the value of [tex]a[/tex] is [tex]0[/tex], which is find out using exponent rule.

Hence, we can say that the value of [tex]a[/tex] is  [tex]0[/tex] .

To know more about probability click here

https://brainly.com/question/219134

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