Question

Simplify x2(y3)4 xy5 = xa ⋅ yb.

Answer 1

Answer:

a = 3 and b = 17

Solution:

Given, x² * (y³)⁴ * x * y⁵ = xᵃ * yᵇ

or, x² * y¹² * x * y⁵ = xᵃ * yᵇ

or, (x² * x) * (y¹² * y⁵) = xᵃ * yᵇ

or, x²⁺¹ * y¹²⁺⁵ = xᵃ * yᵇ

or, x³ * y¹⁷ = xᵃ * yᵇ

∴ comparing the like powers of x and y from both sides, we get

a = 3 and b = 17.

Laws of indices:

• xᵃ * xᵇ = xᵃ⁺ᵇ
• xᵃ * yᵃ = (x * y)ᵃ
• (xᵃ)ᵇ = xᵃᵇ

Answer 2

Answer:

a=1    b=7

Step-by-step explanation:

got it right on assignment