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:

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


Formula 2:

$f(n) = 440 (2)^{\frac{n-49}{12} }$

Answer 1

Answer:

Steps are shown

Step-by-step 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:

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

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:

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

Substitute:

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

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