Answer:
Using exponent rule:
[tex]\frac{1}{a^n}=a^{-n}[/tex]
[tex](a^n)^m = a^{nm}[/tex]
Solve:
[tex](\frac{1}{8})^{-3a} =(512)^{3a}[/tex]
We can write 512 as:
[tex]512 = 8 \cdot 8 \cdot 8 = 8^3[/tex]
then;
[tex](\frac{1}{8})^{-3a} =(8^3)^{3a}[/tex]
⇒[tex](\frac{1}{8})^{-3a} =(8)^{9a}[/tex]
Using exponent rule we have;
⇒[tex](8^{-1})^{-3a} =(8)^{9a}[/tex]
⇒[tex](8)^{3a} =(8)^{9a}[/tex]
On comparing both sides we have;
3a = 9a
⇒9a-3a = 0
⇒6a = 0
⇒a = 0
Therefore, the value of a = 0
