Use Multiplication Properties of Exponents: example 6.25

Simplify: ⓐ ${(5 m)}^{2} (3 m^{3})$ ⓑ ${(3 x^{2} y)}^{4} {(2 x y^{2})}^{3} .$

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: ⓐ ${(5 n)}^{2} (3 n^{10})$ ⓑ ${(c^{4} d^{2})}^{5} {(3 c d^{5})}^{4} .$

How did it go?

ⓐ	${(5 m)}^{2} (3 m^{3})$
Raise $5 m$ to the second power.	$5^{2} m^{2} \cdot 3 m^{3}$
Simplify.	$25 m^{2} \cdot 3 m^{3}$
Use the Commutative Property.	$25 \cdot 3 \cdot m^{2} \cdot m^{3}$
Multiply the constants and add the exponents.	$75 m^{5}$
ⓑ	${(3 x^{2} y)}^{4} {(2 x y^{2})}^{3}$
Use the Product to a Power Property.	$(3^{4} x^{8} y^{4}) (2^{3} x^{3} y^{6})$
Simplify.	$(81 x^{8} y^{4}) (8 x^{3} y^{6})$
Use the Commutative Property.	$81 \cdot 8 \cdot x^{8} \cdot x^{3} \cdot y^{4} \cdot y^{6}$
Multiply the constants and add the exponents.	$648 x^{11} y^{10}$

ⓐ	${(5 m)}^{2} (3 m^{3})$
Raise $5 m$ to the second power.	$5^{2} m^{2} \cdot 3 m^{3}$
Simplify.	$25 m^{2} \cdot 3 m^{3}$
Use the Commutative Property.	$25 \cdot 3 \cdot m^{2} \cdot m^{3}$
Multiply the constants and add the exponents.	$75 m^{5}$
ⓑ	${(3 x^{2} y)}^{4} {(2 x y^{2})}^{3}$
Use the Product to a Power Property.	$(3^{4} x^{8} y^{4}) (2^{3} x^{3} y^{6})$
Simplify.	$(81 x^{8} y^{4}) (8 x^{3} y^{6})$
Use the Commutative Property.	$81 \cdot 8 \cdot x^{8} \cdot x^{3} \cdot y^{4} \cdot y^{6}$
Multiply the constants and add the exponents.	$648 x^{11} y^{10}$