Question

Simplify the expression: (left(Xᵃ/x cdot x⁻ᵇright)ᵃ⁻ᵇ times left(Xᵇ/x cdot x⁻ᶜright)ᵇ⁻ᶜ times left(xᶜ/x cdot x⁻ᵃright)ᶜ⁻ᵃ)

a) (Xᵃ⁺ᵇ⁺ᶜ)

b) (Xᵃ⁻ᵇ⁻ᶜ)

c) (Xᵃ⁻ᵇ⁺ᶜ)

d) (Xᵃ⁺ᵇ⁻ᶜ)

Answer 1

To simplify the expression (Xᵃ/x · x⁻ᵇ)ᵃ⁻ᵇ · (Xᵇ/x · x⁻ᶜ)ᵇ⁻ᶜ · (xᶜ/x · x⁻ᵃ)ᶜ⁻ᵃ, we need to use the properties of exponents and simplify each term. The expression simplifies to (X^b · x^(c-a))^(c-a), which corresponds to option (d).

Step-by-step explanation:

To simplify the expression (Xᵃ/x · x⁻ᵇ)ᵃ⁻ᵇ · (Xᵇ/x · x⁻ᶜ)ᵇ⁻ᶜ · (xᶜ/x · x⁻ᵃ)ᶜ⁻ᵃ, we need to use the properties of exponents.

First, we can multiply the exponents when the bases are the same, which gives us:

(Xᵃ/x)ᵃ⁻ᵇ · (Xᵇ/x)ᵇ⁻ᶜ · (xᶜ/x)ᶜ⁻ᵃ

Next, we can simplify each term individually:

X^(a-(a-b)) · X^(b-(b-c)) · x^(c-(c-a))

Finally, we simplify further:

X^b · X^(c-a) · x^(c-a)

This simplifies to the expression (X^b · x^(c-a))^(c-a), so the correct option is (d) (X^b · x^(c-a))^(c-a).