Question

The value of xᵃ ⁻ ᵇ × xᵇ ⁻ ᶜ × xᶜ ⁻ ᵃ

Answer 1

Answer- The above question is from the chapter 'Exponents and Powers'.

Exponents: Exponent is a mathematical operation in which a number called a base has a power written raised to the base.

Exponent is used to avoid the repetition of numbers being multiplied.

Example:

2 × 2 × 2 = 8

2³ = 8

Here, 2 is the base and 3 is the exponent or power.

Concept used: 1) aⁿ × aˣ = aⁿ⁺ˣ

2) a⁰ = 1

Given question: The value of xᵃ ⁻ ᵇ × xᵇ ⁻ ᶜ × xᶜ ⁻ ᵃ is _____ .

Solution: When bases are same and powers are different in multiplication, the powers get added up i.e. aⁿ × aˣ = aⁿ⁺ˣ .

xᵃ ⁻ ᵇ × xᵇ ⁻ ᶜ × xᶜ ⁻ ᵃ

= xᵃ ⁻ ᵇ ⁺ ᵇ ⁻ ᶜ ⁺ ᶜ ⁻ ᵃ

= x⁰ (∵ a - b + b - c + a = 0)

= 1

∴ The value of xᵃ ⁻ ᵇ × xᵇ ⁻ ᶜ × xᶜ ⁻ ᵃ is 1 .