Use Multiplication Properties of Exponents: example 10.25

Simplify: ${(3 p^{2} q)}^{4} {(2 p q^{2})}^{3} .$

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: ${(u^{3} v^{2})}^{5} {(4 u v^{4})}^{3} .$

How did it go?

	${(3 p^{2} q)}^{4} {(2 p q^{2})}^{3}$
Use the Power of a Product Property.	$3^{4} {(p^{2})}^{4} q^{4} \cdot 2^{3} p^{3} {(q^{2})}^{3}$
Use the Power Property.	$81 p^{8} q^{4} \cdot 8 p^{3} q^{6}$
Use the Commutative Property.	$81 \cdot 8 \cdot p^{8} \cdot p^{3} \cdot q^{4} \cdot q^{6}$
Multiply the constants and add the exponents for each variable.	$648 p^{11} q^{10}$

	${(3 p^{2} q)}^{4} {(2 p q^{2})}^{3}$
Use the Power of a Product Property.	$3^{4} {(p^{2})}^{4} q^{4} \cdot 2^{3} p^{3} {(q^{2})}^{3}$
Use the Power Property.	$81 p^{8} q^{4} \cdot 8 p^{3} q^{6}$
Use the Commutative Property.	$81 \cdot 8 \cdot p^{8} \cdot p^{3} \cdot q^{4} \cdot q^{6}$
Multiply the constants and add the exponents for each variable.	$648 p^{11} q^{10}$