SIMPLIFYING EXPRESSIONS WITH NEGATIVE EXPONENTS WORKSHEET

Question 1 :

Simplify : 

x⁵(x^-2)^-3

Question 2 :

Simplify : 

x[x⁴(x^-3)²]^-5

Question 3 :

Simplify : 

y^-4(y³)^-5

Question 4 :

Simplify : 

t⁴[t³(t^-2)⁵]⁴

Question 5 :

Simplify : 

y⁴[y^-2(y⁵)²]^-3

Question 6 :

Simplify : 

w³[w⁴(w^-3)⁶]²

Detailed Answer Key

Question 1 :

Simplify : 

x⁵(x^-2)^-3

Solution :

=  x⁵(x^-2)^-3

=  x⁵ ⋅ x⁶

=  x^{5 + 6} 

=  x¹¹ 

Question 2 :

Simplify : 

x[x⁴(x^-3)²]^-5

Solution :

=  x[x⁴(x^-3)²]^-5

=  x[x⁴(x^-6)]^-5

=  x(x^{4 - 6})^-5

=  x(x^-2)^-5

=  x(x¹⁰)

=  x^{1 + 10}

=  x¹¹

Question 3 :

Simplify : 

y^-4(y³)^-5

Solution :

=  y^-4(y³)^-5

=  y^-4(y^-15)

=  y^{-4 - 15}

=  y^-19

=  1/y¹⁹

Question 4 :

Simplify : 

t⁴[t³(t^-2)⁵]⁴

Solution :

=  t⁴[t³(t^-2)⁵]⁴

=  t⁴[t³(t^-10)]⁴

=  t⁴(t^{3 - 10})⁴

=  t⁴(t^-7)⁴

=  t⁴(t^-28)

=  t^{4 - 28}

=  t^-24

  =  1/t²⁴

Question 5 :

Simplify : 

y⁴[y^-2(y⁵)²]^-3

Solution :

=  y⁴[y^-2(y⁵)²]^-3

=  y⁴[y^-2(y¹⁰)]^-3

=  y⁴(y^{-2 + 10})^-3

=  y⁴(y⁸)^-3

=  y⁴(y^-24)

=  y^{4 -24}

=  y^-20

=  1/y²⁰

Question 6 :

Simplify : 

w³[w⁴(w^-3)⁶]²

Solution :

=  w³[w⁴(w^-3)⁶]²

=  w³[w⁴(w^-18)]²

=  w³(w^{4 - 18})²

=  w³(w^-14)²

=  w³(w^-28)

=  w^{3 - 28}

=  w^-25

=  1/w²⁵

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