Answer:
x = - [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^m}[/tex]
Note that 16 = 4² and 64 = 4³ , then
[tex]16^{x}[/tex] = [tex]\frac{1}{64}[/tex] , can be expressed as
[tex](4^2)^{x}[/tex] = [tex]\frac{1}{4^3}[/tex] , that is
[tex]4^{2x}[/tex] = [tex]4^{-3}[/tex]
Since the bases on both sides are equal, then equate the exponents
2x = - 3 ( divide both sides by 2 )
x = - [tex]\frac{3}{2}[/tex]
