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 :

=  36t^6 ⋅ 2

=  36t¹²

Example 3 :

Simplify :

(5c⁷)²

Solution :

=  (5c⁷)²

Power of a Product Property : 

=  (5)²(c⁷)²

Power of a Power Property :

=  25c^7 ⋅ 2

=  25c¹⁴

Example 4 :

Simplify :

(10t³)³

Solution :

=  (10t³)³

Power of a Product Property : 

=  (10)³(t³)³

Power of a Power Property :

=  1000t^{3 ⋅ 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 :

=  5.0625u^{3 ⋅ 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 :

=  625n^{4 ⋅ 4}

=  625n¹⁶

Example 7 :

Simplify :

(4y⁹)⁴

Solution :

=  (4y⁹)⁴

Power of a Product Property : 

=  (4)⁴(y⁹)⁴

Power of a Power Property :

=  256y^{9 ⋅ 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 :

=  144a^{2 ⋅ 2}b^{6 ⋅ 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 :

=  125x^{5 ⋅ 3}y³

=  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 :

=  16p^{5 ⋅ 4}q^{2 ⋅ 4}r^{3 ⋅ 4}

=  16p²⁰q⁸r¹²

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