🔎 Fractions + Exponents = Need Parentheses!

When doing internal rate of return problems and yield to maturity problems, we sometimes have to take the exponent of a number, but the exponent is a fraction.

For example, we might have to calculate

$$1.56^{\frac13}$$

When you enter this into a calculator or spreadsheet, you have to be careful.

There are two approaches you can use:

1. Calculate the fraction in advance (as a decimal number)
2. Use parentheses

Note that if you just calculate 1.56^1/3 in a spreadsheet (or press the corresponding buttons on a calculator), you will get the wrong answer. You don’t want to make an error like this!

1 - Calculate the fraction in advance

One way to calculate $1.56^{\frac13}$ is to calculate $\frac13 = .3333$ in advance. Then you just calculate 1.56^.3333 in a spreadsheet (or press the corresponding buttons on a calculator).

Easy as pie!

Notes:

• To do this with a calculator, you’ll typically press the x^y or the y^x button where I included a caret: ^. Essentially, x^y, y^x, and ^ all mean the same thing.
• I wrote out four digits in .3333. You could probably get away with just three digits, but four digits isn’t hard at all and you’ll get a more accurate number.

2 - Use parentheses

Instead of calculating the fraction out in advance, you can use parentheses to tell your calculator or spreadsheet to calculate the fraction first.

On a spreadsheet, you’d write, 1.56^(1/3).

Don’t forget the parentheses! Remember, 1.56^1/3=0.52 (wrong answer), but 1.56^(1/3)=1.16 (right answer).

Similarly, with a calculator, you’d type 1.56 y^x (1/3). Again, don’t forget the parentheses!