Question

Simplify each expression

Answer 1

The correct answer is

(2m³n²)³/(-18m⁵n⁴) = - m⁴n²/9

Explanation:

It is given an expression,

(2m³n²)³/(-18m⁵n⁴)

Points to remember

Identities

1). (xᵃ)ᵇ = xᵃᵇ

2). xᵃ/xᵇ = xᵃ⁻ᵇ

To solve the expression

(2m³n²)³/(-18m⁵n⁴) = -2m⁹n⁶/18m⁵n⁴ (Using identity 1)

= -2/18(m⁹⁻⁵n⁶⁻⁴) (Using identity 2)

= -1/9(m⁴n²)

= - m⁴n²/9

Therefore the simplified form of given expression is given by,

(2m³n²)³/(-18m⁵n⁴) = - m⁴n²/9

Answer 2

`-(4m^(4)n^(2))/(9)`

Explanation:

The given expression is

`=((2m^3n^2)^3)/(-18m^5n^4)`

Use the power rule of indices on the denominator;
`(a^m)^n=a^(mn)`

`=(8m^9n^6)/(-18m^5n^4)`

We apply the quotient rule of indices;
`(a^m)/(a^n) =a^(m-n)`

`=(8m^9n^6)/(-18m^5n^4)`

`=-(4m^(9-5)n^(6-4))/(9)`

Simplify

`=-(4m^(4)n^(2))/(9)`