Question

Evaluate the expression. 2 13 21 The value of the expression is

Answer 1

To solve the exercise you can use the following property of powers

`((a)/(b))^n=(a^n)/(b^n)`

Then, you have

`\begin{gathered} |((-1)/(2))^3/((1)/(4))^2|=|((-1)^3)/((2)^3)^{}/((1)^2)/((4)^2)^{}| \\ |((-1)/(2))^3/((1)/(4))^2|=|\frac{-1^{}}{8}^{}/(1)/(16)^{}| \end{gathered}`

Now, apply the definition of fractional division, that is

`(a)/(b)/(c)/(d)=(a\cdot d)/(b\cdot c)`
`\begin{gathered} |((-1)/(2))^3/((1)/(4))^2|=|\frac{-1^{}\cdot16}{8\cdot1}^{}| \\ |((-1)/(2))^3/((1)/(4))^2|=|\frac{-1^{}6}{8}^{}| \\ |((-1)/(2))^3/((1)/(4))^2|=|-2| \end{gathered}`

Finally, apply the definition of absolute value, that is, it is the distance between a number and zero. The distance between -2 and 0 is 2.

Therefore, the value of the expression is 2.

`\begin{gathered} |((-1)/(2))^3/((1)/(4))^2|=|-2| \\ |((-1)/(2))^3/((1)/(4))^2|=2 \end{gathered}`