Question

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

Answer 1

16

Explanation:

Given expression:

`\left(-(1)/(2)\right)^(-4)`

`\textsf{Apply exponent rule} \quad a^(-n)=(1)/(a^n):`

`\implies (1)/(\left(-(1)/(2)\right)^(4))`

`\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}:`

`\implies (1)/(\left((1)/(2)\right)^(4))`

`\textsf{Apply exponent rule} \quad \left((a)/(b)\right)^c=(a^c)/(b^c):`

`\implies (1)/(\left((1^4)/(2^4)\right))`

`\implies (1)/(\left((1)/(16)\right))`

`\textsf{Apply the fraction rule} \quad (1)/((b)/(c))=(c)/(b):`

`\implies (16)/(1)`

`\implies 16`

Answer 2

• 16

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