Sample Problems: Laws of Exponents

Problem 1: Find the value of 2^-3

Solution:

Problem 2: 

Solution:

Problem 3: Simplify using above properties: 

(-4)⁵ x (-4)^-10

Solution:

(-4)⁵ x (-4)^-10

= -4^(5-10)                     (a^m × aⁿ = a^m+n)

= (-4)^-5

Problem 4: Simplify using above properties: 

Solution:

Problem 5: Simplify, 

Solution:

Problem 6: What is the 5th root of 5¹⁵. 

Solution:

We know that nth of a number “a” is represented by 

Thus, 5th of 5¹⁵ will be given by, 

= 5³

= 125

Problem 7: Find the value of n 

Solution:

⇒ 2^n-3 × 2^{4n – 16} = 1 

⇒ 2^{n – 3 + 4n – 16} = 2⁰

Comparing Both Sides

n – 3 + 4n -16 = 0 

⇒ 5n -19 = 0 

⇒ n =

Laws of Exponents are fundamental rules used in mathematics to simplify expressions involving exponents. These laws help in solving arithmetic problems efficiently by defining operations like multiplication, division, and more on exponents. In this article, we will discuss the laws of exponent for real number in detail with some solved examples.