Use Multiplication Properties of Exponents: example 6.24

Simplify: ⓐ ${(y^{3})}^{6} {(y^{5})}^{4}$ ⓑ ${(−6 x^{4} y^{5})}^{2} .$

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: ⓐ ${(a^{4})}^{5} {(a^{7})}^{4}$ ⓑ ${(−2 c^{4} d^{2})}^{3} .$

How did it go?

ⓐ	${(y^{3})}^{6} {(y^{5})}^{4}$
Use the Power Property.	$y^{18} \cdot y^{20}$
Add the exponents.	$y^{38}$
ⓑ	${(−6 x^{4} y^{5})}^{2}$
Use the Product to a Power Property.	${(−6)}^{2} {(x^{4})}^{2} {(y^{5})}^{2}$
Use the Power Property.	${(−6)}^{2}$
Simplify.	$36 x^{8} y^{10}$

ⓐ	${(y^{3})}^{6} {(y^{5})}^{4}$
Use the Power Property.	$y^{18} \cdot y^{20}$
Add the exponents.	$y^{38}$
ⓑ	${(−6 x^{4} y^{5})}^{2}$
Use the Product to a Power Property.	${(−6)}^{2} {(x^{4})}^{2} {(y^{5})}^{2}$
Use the Power Property.	${(−6)}^{2}$
Simplify.	$36 x^{8} y^{10}$