SIMPLIFYING EXPRESSIONS WITH POWERS

We can use the following properties of exponents to simplify expressions with powers. 

Solved Examples

Example 1 :

Simplify : 

(x³)²

Solution : 

=  (x³)²

=  x ^{3 ⋅ 2}

=  x ⁶

Example 2 :

Simplify :

x³ ⋅ x⁵

Solution :  

=  x³ ⋅ x⁵

=  x^{3 + 5}

=  x ⁸

Example 3 :

Simplify : 

m⁰ · m^-3 · m⁵

Answer : 

=  m⁰ · m^-3 · m⁵

=  1 · m^{-3 + 5}

=  m²

Example 4 :

Simplify : 

x⁸ / x⁵

Solution : 

=  x⁸ / x⁵

=  x^{8 - 5}

=  x³

Example 5 :

Simplify : 

4x⁵ / 8x⁷

Solution : 

=  4x⁵ / 8x⁷

=  x⁵ / 2x⁷

=  x^{5 - 7} / 2

=  x^-2 / 2

=  1 / (2x²)

Example 6 :

Simplify : 

(121m⁶)^1/2

Solution :

=  (121m⁶)^1/2

=  (11 ⋅ 11 ⋅ m⁶)^1/2

=  (11² ⋅ m⁶)^1/2

=  (11²)^1/2 ⋅ (m⁶)^1/2

=  11^{2 ⋅ 1/2} ⋅ m^{6 ⋅ 1/2}

=  11¹ ⋅ m³

=  11m³

Example 7 :

Simplify : 

(9n⁴)^1/2

Solution :

=  (9n⁴)^1/2

=  (3² ⋅ n⁴)^1/2

=  (3²)^1/2 ⋅ (n⁴)^1/2

=  3^{2 ⋅ 1/2} ⋅ n^{4 ⋅ 1/2}

=  3¹ ⋅ n²

=  3 ⋅ n²

=  3n²

Example 8 :

Simplify : 

(8x³y⁶)^1/3

Solution :

=  (8x³y⁶)^1/3

=  (2³ ⋅ x³ ⋅ y⁶)^1/3

=  (2³)^1/3 ⋅ (x³)^1/3 ⋅ (y⁶)^1/3 

=  2^{3 ⋅ 1/3} ⋅ x^{3 ⋅ 1/3} ⋅ y^{6 ⋅ 1/3} 

=  2¹ ⋅ x¹ ⋅ y²

=  2xy²

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.