# How do you simplify (13r^7)/(39r^4)?

Apr 28, 2017

$\frac{{r}^{3}}{3}$

#### Explanation:

You can write down tour equation again:

$\frac{13 \cdot {r}^{4} \cdot {r}^{3}}{3 \cdot 13 \cdot {r}^{4}}$

Now $13 {r}^{4}$s cancel each other

You get

${r}^{3} / 13$

This is your answer ${r}^{3} / 13$

Apr 28, 2017

$\frac{13 {r}^{3}}{39}$

#### Explanation:

$\textcolor{b l u e}{\text{First principle method}}$

Note that 13 is a prime number so you can not simplify any further the value of $\frac{13}{39}$

Write as: $\text{ } \frac{13}{39} \times \frac{{r}^{4} \times {r}^{3}}{r} ^ 4$

$\text{ } \frac{13}{39} \times {r}^{4} / {r}^{4} \times {r}^{3}$

But ${r}^{4} / {r}^{4} = 1$ giving:

$\text{ } \frac{13}{39} \times 1 \times {r}^{3}$

$\text{ } \frac{13 {r}^{3}}{39}$
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$\textcolor{b l u e}{\text{Shortcut method}}$

$\frac{13 {r}^{7}}{39 {r}^{4}} \text{ "=" "(13r^(7-4))/39" } = \frac{13 {r}^{3}}{39}$