Question

[(xy)²]² X x³ y³ ÷ x⁴ y⁵ : Simplify.

Answer 1

Answer ⇒ x³y²

Solution ⇒

Given conditions ⇒

[(xy)²]² × x³ y³ ÷ x⁴ y⁵ [∵ (xy)ᵃ = xᵃ.yᵃ]

= x⁴y⁴ × x³y³ ÷ x⁴y⁵

= x⁴x³× y⁴y³ ÷ x⁴y⁵

= x⁴ ⁺ ³. y⁴ ⁺ ³ ÷ x⁴y⁵ [xᵃ.xᵇ = xᵃ ⁺ ᵇ]

= x⁷y⁷ ÷ x⁴y⁵

= x⁷ ⁻ ⁴. y⁷ ⁻ ⁵ [ ∵ xᵃ/xᵇ = xᵃ ⁻ ᵇ ]

= x³.y²

Hope it helps.

Answer 2

Acc to the question, we have to simplify: [(xy)²]² × x³ y³ ÷ x⁴ y⁵

or, $x^{4} y^{4}$ × x³ y³ ÷ x⁴ y⁵

or, $x^{4} y^{4}$ × $x^{-1} y^{-2}$

or, x³y²[Ans]

basically, we have to apply the basic concept of laws of indices and subtract the power in case of division and add the power in case of multiplication, provided both have same base.

Therefore, [(xy)²]² X x³ y³ ÷ x⁴ y⁵ = x³y²