Question

1/16^3x=64^2(x+8) Solve for x.

Answer 1

Answer:

x = -4

Step-by-step explanation:

16 = 4*4 = 4²

64 = 4 * 4* 4 = 4³

$(\dfrac{1}{16})^{3x}=64^{2*(x+8)}\\\\\\(16^{-1})^{3x}=64^{2x + 16}\\\\\\16^{-3x}=64^{2x +16}\\\\(4^{2})^{-3x}=(4^{3})^{2x+16}\\\\4^{-6x}=4^{6x +48}$

As bases are same, compare exponents

6x + 48 = -6x  

Subtract 48 from both sides

6x = -6x - 48

Add '6x' to both sides

6x + 6x = -48

12x = -48

Divide both sides by 12

x = -48/12

x = -4