Question

Which expression is equivalent to..? Assume

Answer 1

Answer:

The equivalent ratio of (3m⁻²n)⁻³/6mn⁻² = m⁵/2n

Step-by-step explanation:

Points to remember

Identities

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

(xᵃ)ᵇ = xᵃᵇ

x⁻ᵃ = 1/xᵃ

To find the equivalent ratio of (3m⁻²n)⁻³/6mn⁻²

By using identities,

(3m⁻²n)⁻³ = 3m⁶n⁻³

(3m⁻²n)⁻³/6mn⁻² = 3m⁶n⁻³/6mn⁻²

 =  3m⁽⁶⁻¹⁾n⁽⁻³ ⁻ ⁻²⁾/6

 = m⁵n⁻¹/2

 = m⁵/2n

Therefore the equivalent ratio of (3m⁻²n)⁻³/6mn⁻² = m⁵/2n