POWERS OF MONOMIALS
In this section, you will learn how to simplify powers of monomials using Properties of Exponents.
Example 1 :
Simplify :
(2u)5
Solution :
= (2u)5
Power of a Product Property :
= (2)5(u)5
= 32u5
Example 2 :
Simplify :
(6t6)2
Solution :
= (6t6)2
Power of a Product Property :
= (6)2(t6)2
Power of a Power Property :
= 36t6 ⋅ 2
= 36t12
Example 3 :
Simplify :
(5c7)2
Solution :
= (5c7)2
Power of a Product Property :
= (5)2(c7)2
Power of a Power Property :
= 25c7 ⋅ 2
= 25c14
Example 4 :
Simplify :
(10t3)3
Solution :
= (10t3)3
Power of a Product Property :
= (10)3(t3)3
Power of a Power Property :
= 1000t3 ⋅ 3
= 1000t9
Example 5 :
Simplify :
(1.5u3)4
Solution :
= (1.5u3)4
Power of a Product Property :
= (1.5)4(u3)4
Power of a Power Property :
= 5.0625u3 ⋅ 4
= 5.0625u12
Example 6 :
Simplify :
(5n4)4
Solution :
= (5n4)4
Power of a Product Property :
= (5)4(n4)4
Power of a Power Property :
= 625n4 ⋅ 4
= 625n16
Example 7 :
Simplify :
(4y9)4
Solution :
= (4y9)4
Power of a Product Property :
= (4)4(y9)4
Power of a Power Property :
= 256y9 ⋅ 4
= 256y36
Example 8 :
Simplify :
(12a2b6)2
Solution :
= (12a2b6)2
Power of a Product Property :
= (12)2(a2)2(b6)2
Power of a Power Property :
= 144a2 ⋅ 2b6 ⋅ 2
= 144a4b12
Example 9 :
Simplify :
(5x5y)3
Solution :
= (5x5y)3
Power of a Product Property :
= (5)3(x5)3(y)3
Power of a Power Property :
= 125x5 ⋅ 3y3
= 125x15y3
Example 10 :
Simplify :
(2p5q2r3)4
Solution :
= (2p5q2r3)4
Power of a Product Property :
= (2)4(p5)4(q2)4(r3)4
Power of a Power Property :
= 16p5 ⋅ 4q2 ⋅ 4r3 ⋅ 4
= 16p20q8r12
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