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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q.463R (page 562)

In the following exercises, divide the monomials.
$72 p^{12} 梅 8 p^{3}$ .

Short Answer

Expert verified

The simplified form is $9 p^{9}$ .

Step by step solution

01

Step 1

Some properties of exponents:

$\frac{a^{m}}{a^{n}} = a^{m - n}, m > n \frac{a^{m}}{a^{n}} = a^{n - m}, n > m$

$a^{m} 路 a^{n} = a^{m + n}$

02

Step 2

Simplify $72 p^{12} 梅 8 p^{3}$ .

Write it in fraction form - role="math" localid="1644925116653" $\frac{72 p^{12}}{8 p^{3}}$ .

Use the fraction multiplication-role="math" localid="1644925092957" $\frac{72}{8} 路 \frac{p^{12}}{p^{3}}$ .

Use quotient property and simplify- role="math" localid="1644925101906" $9 路 p^{12 - 3} = 9 p^{9}$ .

So, $\frac{72 p^{12}}{8 p^{3}} = 9 p^{9}$ .

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