Find the value of x⁻³ if x = (100)¹⁻⁴ ÷ (100)⁰

The value of x⁻³ if x = (100)¹⁻⁴ ÷ (100)⁰ is (100)⁹ using the law of exponents a° = 1, where a ≠ 0 and (am)n = amn

Find the value of x^-3 if x = (100)^{1 - 4} ÷ (100)⁰.

Solution:

Given, the expression is x = (100)^{1 - 4} ÷ (100)⁰.

We have to find the value of x^-3.

(100)^{1 - 4} = (100)^-3

a⁰ = 1, where a ≠ 0

(100)⁰ = 1

Now, x = (100)^{1 - 4} ÷ (100)⁰

x = (100)^-3 ÷ 1

x = (100)^-3

To find x^-3,

x^-3 = [(100)^-3]^-3

Using law of exponents,

(a^m)ⁿ = a^mn

So, x^-3 = (100)^{-3x - 3}

= (100)⁹

Therefore, the value of x^-3 is (100)⁹.

✦ Try This: Find the value of x^-3 if x = (11)^{1 - 3} ÷ (11)⁰.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 101

Summary:

The value of x^-3 if x = (100)^{1 - 4} ÷ (100)⁰ is (100)⁹ using the law of exponents a⁰ = 1, where a ≠ 0 and (a^m)ⁿ = a^mn

☛ Related Questions:

Math worksheets and
visual curriculum