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What is the value of (-1/2)to the power of -4

Sagot :

mhanifa

Answer:

  • 16

Step-by-step explanation:

Use the following properties

  • (- a)²ᵇ = a²ᵇ
  • (1/a)⁻ᵇ = aᵇ

Find the value of the given expression

  • (-1/2)⁻⁴ = (- 2)⁴ = 2⁴ = 16
semsee45

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]

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