Question

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Formula 1 can be written alternatively as formula 2. Use algebra to show your steps how formula 1 can be manipulated to create formula 2.


Formula 1:


`f(n)=\left\\ ({\sqrt[{12}]{2}}\,\right)^(n-49)* 440\,{\text{Hz}}\,}`


Formula 2:


`f(n) = 440 (2)^{(n-49)/(12) }`

Answer 1

Steps are shown

Explanation:

Exponent Rules

We need to recall this fundamental rule for exponents:

`\displaystyle \sqrt[n]{a^m}=a^(m/n)`

We are given the expression:

`f(n)=\left ({\sqrt[{12}]{2}}\,\right)^(n-49)* 440\,{\text{Hz}}`

We'll use algebra and the above rule to manipulate the expression.

First, get rid of the unit Hz and move the coefficient 440 to the left:

`f(n)=440\left ({\sqrt[{12}]{2}}\,\right)^(n-49)`

Now we convert the radical into an exponent form:

`\displaystyle \left ({\sqrt[{12}]{2}}\,\right)^(n-49)=(2)^{(n-49)/(12)}`

Substitute:

`f(n)=440\left ({\sqrt[{12}]{2}}\,\right)^(n-49)=440~(2)^{(n-49)/(12)}`

This is the very same expression in formula 2, as required.