Divide Monomials: example 6.71

Simplify: $\frac{{(10 p^{3})}^{2}}{{(5 p)}^{3} {(2 p^{5})}^{4}} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify: $\frac{{(3 r^{3})}^{2} {(r^{3})}^{7}}{{(r^{3})}^{3}} .$

How did it go?

	$\frac{{(10 p^{3})}^{2}}{{(5 p)}^{3} {(2 p^{5})}^{4}}$
Use the Product to a Power Property, ${(a b)}^{m} = a^{m} b^{m}$ .	$\frac{{(10)}^{2} {(p^{3})}^{2}}{{(5)}^{3} {(p)}^{3} {(2)}^{4} {(p^{5})}^{4}}$
Use the Power Property, ${(a^{m})}^{n} = a^{m \cdot n}$ .	$\frac{100 p^{6}}{125 p^{3} \cdot 16 p^{20}}$
Add the exponents in the denominator.	$\frac{100 p^{6}}{125 \cdot 16 p^{23}}$
Use the Quotient Property, $\frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}}$ .	$\frac{100}{125 \cdot 16 p^{17}}$
Simplify.	$\frac{1}{20 p^{17}}$

	$\frac{{(10 p^{3})}^{2}}{{(5 p)}^{3} {(2 p^{5})}^{4}}$
Use the Product to a Power Property, ${(a b)}^{m} = a^{m} b^{m}$ .	$\frac{{(10)}^{2} {(p^{3})}^{2}}{{(5)}^{3} {(p)}^{3} {(2)}^{4} {(p^{5})}^{4}}$
Use the Power Property, ${(a^{m})}^{n} = a^{m \cdot n}$ .	$\frac{100 p^{6}}{125 p^{3} \cdot 16 p^{20}}$
Add the exponents in the denominator.	$\frac{100 p^{6}}{125 \cdot 16 p^{23}}$
Use the Quotient Property, $\frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}}$ .	$\frac{100}{125 \cdot 16 p^{17}}$
Simplify.	$\frac{1}{20 p^{17}}$