Exercises: Simple fractions

Set up the term

First, you need to "translate" the text in the task into a mathematical term:

Now you put this together to a term.

If you write the division with the divide-by sign, you get:

$6^4:(9\cdot 16)$

(Important: Around "$9\cdot 16$" you have to write a parenthesis, because otherwise it would be divided only by $9$ and not by $9\cdot 16$).

If you write the division with the fraction bar, you get:

${\displaystyle \frac{6^4}{9\cdot 16}}$

(You don't need to put parentheses here because the fraction bar acts like a parenthesis).

Calculate term

1st way:

Now calculate the term:

${\displaystyle \frac{6^4}{9\cdot 16}}$$={\displaystyle \frac{1296}{144}}$

Since 1296 is a multiple of 144, you can shorten the fraction by 144.

${\displaystyle \frac{6^4}{9\cdot 16}}={\displaystyle \frac{1296}{144}}=9$

2nd way:

${\displaystyle \frac{6^4}{9\cdot 16}}={\displaystyle \frac{(2\cdot 3{)}^4}{3^2\cdot 2^4}}$

${\displaystyle \frac{2^4\cdot 3^4}{3^2\cdot 2^4}}={\displaystyle \frac{\cancel{2^4}\cdot 3^4}{3^2\cdot \cancel{2^4}}}={\displaystyle \frac{3^4}{3^2}}=3^{(4-2)}$ apply the power laws

$3^2=9$