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Rational Exponents — Part 2

Source: Canadian Money and Business Diagram - alfexe/iStock/Getty Images

Investing Money

One formula that can be used to calculate the amount of money earned from an investment is

\[F=P(1+i)^n\]

Piggy bank on top of books.

Source: Piggy Bank - seb_ra/iStock/Getty Images

Investing Money — Continued

To calculate the future value of an investment made for \(8\) months, the formula becomes:

\[F=P(1+i)^{2/3}\]

Since \(8\) months is \(\dfrac{8}{12} = \dfrac{2}{3}\) years, the formula has an exponent that is a rational number.

Piggy bank on top of books.

Source: Piggy Bank - seb_ra/iStock/Getty Images

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Lesson Goals

  • Simplify and evaluate positive rational exponents of the form \(\dfrac{a}{n}\).
  • Simplify and evaluate negative rational exponents of the form \(\dfrac{-a}{n}\).

Try This!

On a particular type of pavement, the braking distance \(d\) (in metres) for a car travelling at a speed of \(v\) kilometres per hour is given by 

\[d=\dfrac{1}{5000}v^\frac{5}{2}\]

What is the braking distance for a car travelling at \(100\) kilometres per hour?