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

Answer:

Using exponent rule:

$\frac{1}{a^n}=a^{-n}$

$(a^n)^m = a^{nm}$

Solve:

$(\frac{1}{8})^{-3a} =(512)^{3a}$

We can write 512 as:

$512 = 8 \cdot 8 \cdot 8 = 8^3$

then;

$(\frac{1}{8})^{-3a} =(8^3)^{3a}$

⇒$(\frac{1}{8})^{-3a} =(8)^{9a}$

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