Question

Simplify each expression

Answer 1

Answer:

$-\frac{4m^{4}n^{2}}{9}$

Step-by-step explanation:

The given expression is

$=\frac{(2m^3n^2)^3}{-18m^5n^4}$

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

$=\frac{8m^9n^6}{-18m^5n^4}$

We apply the quotient rule of indices; $\frac{a^m}{a^n} =a^{m-n}$

$=\frac{8m^9n^6}{-18m^5n^4}$

$=-\frac{4m^{9-5}n^{6-4}}{9}$

Simplify

$=-\frac{4m^{4}n^{2}}{9}$

Answer 2

Answer:

The correct answer is

(2m³n²)³/(-18m⁵n⁴) = - m⁴n²/9

Step-by-step 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