# How do you simplify (9pq^9r^5s^9)(7pq^7rs^5)?

$63 {p}^{2} {q}^{16} {r}^{6} {s}^{14}$

#### Explanation:

When dealing with a problem like this, we look at each variable separately (and the constants also) and so something that looks long and scary can be broken down into little bits and worked on.

So we have:

$\left(9 p {q}^{9} {r}^{5} {s}^{9}\right) \left(7 p {q}^{7} r {s}^{5}\right)$

Now everything here is being multiplied, so I can rewrite the above this way:

$9 \times p \times {q}^{9} \times {r}^{5} \times {s}^{9} \times 7 \times p \times {q}^{7} \times r \times {s}^{5}$

and rearrange the values like this:

$9 \times 7 \times p \times p \times {q}^{9} \times {q}^{7} \times {r}^{5} \times r \times {s}^{9} \times {s}^{5}$

and so now it's easier to combine the constants and variables with each other. I'll use brackets to help in organizing them:

$\left(9 \times 7\right) \times \left(p \times p\right) \times \left({q}^{9} \times {q}^{7}\right) \times \left({r}^{5} \times r\right) \times \left({s}^{9} \times {s}^{5}\right)$

$\left(63\right) \times \left({p}^{2}\right) \times \left({q}^{16}\right) \times \left({r}^{6}\right) \times \left({s}^{14}\right)$

And now we can remove the brackets to end up with:

$63 {p}^{2} {q}^{16} {r}^{6} {s}^{14}$