# How do you simplify (5/8)^2?

$\frac{25}{64}$

#### Explanation:

With this question, it looks confusing - what do I do with the 5 and the - do I multiply just one or both? But if we remember that when we square something we are simply multiplying by itself, that might help clear up any confusion.

Starting with the original:

${\left(\frac{5}{8}\right)}^{2}$

we can rewrite this as:

$\left(\frac{5}{8}\right) \left(\frac{5}{8}\right)$

a quick bit of multiplication gets us:

$\left(\frac{5}{8}\right) \left(\frac{5}{8}\right) = \frac{25}{64}$

So when faced with the original again:

${\left(\frac{5}{8}\right)}^{2}$

we can also see that we can write it this way:

${\left(\frac{5}{8}\right)}^{2} = {5}^{2} / {8}^{2} = \frac{25}{64}$

Both are correct ways to view this and get to the same result.

Jul 5, 2016

$\frac{25}{64}$

#### Explanation:

Going about it the long way so that you can see where the shortcut comes from.

Consider ${2}^{2}$ this is $2 \times 2 = 4$

But you can if you wish (not normally done) write this as:

${\left(\frac{2}{1}\right)}^{2} \text{ " =" " 2/1xx2/1" " =" " (2xx2)/(1xx1)" " =" " 4/1" "=" } 4$

Lets use the same process for your question:

${\left(\frac{5}{8}\right)}^{2} \text{ " =" " 5/8xx5/8" " =" "(5xx5)/(8xx8)" " =" } \frac{25}{64}$
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$\textcolor{b l u e}{\text{Shortcut method}}$

${\left(\frac{5}{8}\right)}^{2} = {5}^{2} / {8}^{2} = \frac{25}{64}$