Answer:
16
Step-by-step explanation:
Given expression:
[tex]\left(-\dfrac{1}{2}\right)^{-4}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{1}{\left(-\dfrac{1}{2}\right)^{4}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}:[/tex]
[tex]\implies \dfrac{1}{\left(\dfrac{1}{2}\right)^{4}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]
[tex]\implies \dfrac{1}{\left(\dfrac{1^4}{2^4}\right)}[/tex]
[tex]\implies \dfrac{1}{\left(\dfrac{1}{16}\right)}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{1}{\frac{b}{c}}=\dfrac{c}{b}:[/tex]
[tex]\implies \dfrac{16}{1}[/tex]
[tex]\implies 16[/tex]
