PROBLEMS WITH NEGATIVE EXPONENTS

Simplify. Your answer should contain only positive exponents.

Problem 1 :

(x^-2 x^-3)⁴

Solution :

Given, (x^-2 x^-3)⁴

= (x^-5)⁴

= x^-20

Problem 2 :

(x⁴)^-3 ⋅ 2x⁴

Solution :

Given, (x⁴)^-3 ⋅ 2x⁴

= x^4(-3) ⋅ 2x⁴

= x^-12 ⋅ 2x⁴

= 2 ⋅ x^-12 ⋅ x⁴

= 2 ⋅ x^-8

Problem 3 :

(n³)³ ⋅ 2n^-1

Solution :

Given, (n³)³ ⋅ 2n^-1

= n ^{(3 ⋅ 3)} ⋅ 2n^-1

= n⁹ ⋅ 2n^-1

= 2n⁹ ⋅ n^-1

= 2n⁸

Problem 4 :

(2v)²  ⋅ 2v²

Solution :

Given, (2v)²  ⋅ 2v²

= 2² ⋅ v² ⋅ 2v²

= 4v² ⋅ 2v²

= 8v⁴

Problem 5 :

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Problem 6 :

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Problem 7 :

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Problem 8 :

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Problem 9 :

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Problem 10 :

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Problem 11 :

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Problem 12 :

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Problem 13 :

(a^-3 b^-3)⁰

Solution :

Given, (a^-3 b^-3)⁰

= (a^-3)⁰ ⋅ (b^-3)⁰

= 1 ⋅  1

= 1

Problem 14 :

x⁴ y³ ⋅ (2y²)⁰

Solution :

Given,  x⁴ y³ ⋅ (2y²)⁰

=  x⁴ y³  ⋅ 1

= x⁴ y³

Problem 15 :

ba⁴ ⋅ (2ba⁴)^-3

Solution :

Given, ba⁴ ⋅ (2ba⁴)^-3

= ba⁴ ⋅ 2^-3 ⋅ b^-3 ⋅ (a⁴)^-3

= ba⁴ ⋅ 2^-3 ⋅ b^-3 ⋅ a^-12 

= b^-2  ⋅ 2^-3 ⋅ a^-8

Problem 16 :

(2x⁰y²)^-3 ⋅ 2yx³

Solution :

Given, (2x⁰y²)^-3 ⋅ 2yx³