Answer:
x = - 5
Step-by-step explanation:
Using the rule of exponents
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
Given
[tex](1/2)^{x}[/tex] = 32
[tex]\frac{1}{2^{x} }[/tex] = 32
[tex]2^{-x}[/tex] = [tex]2^{5}[/tex]
Since the bases are equal, both 5, equate the exponents
Hence x = - 5
