Question

Solve (1/8)^-3a=512^3a

Answer 1

Solve (1/8)^-3a = 512^3a
A=0

I took the assignment it’s right.

Answer 2

Using exponent rule:

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

`(a^n)^m = a^(nm)`

Solve:

`((1)/(8))^(-3a) =(512)^(3a)`

We can write 512 as:

`512 = 8 \cdot 8 \cdot 8 = 8^3`

then;

`((1)/(8))^(-3a) =(8^3)^(3a)`

⇒
`((1)/(8))^(-3a) =(8)^(9a)`

Using exponent rule we have;

⇒
`(8^(-1))^(-3a) =(8)^(9a)`

⇒
`(8)^(3a) =(8)^(9a)`

On comparing both sides we have;

3a = 9a

⇒9a-3a = 0

⇒6a = 0

⇒a = 0

Therefore, the value of a = 0