Question

Which expression is equivalent

Answer 1

Correct choice is B

Explanation:

Consider expression

`((3m^(-1)n^2)^4)/((2m^(-2)n)^3).`

1. Simplify numerator:

`(3m^(-1)n^2)^4=3^4\cdot (m^(-1))^4\cdot (n^2)^4=81m^(-4)n^8.`

2. Simplify denominator:

`(2m^(-2)n)^3=2^3\cdot (m^(-2))^3\cdot n^3=8m^(-6)n^3.`

Then,

`((3m^(-1)n^2)^4)/((2m^(-2)n)^3)=(81m^(-4)n^8)/(8m^(-6)n^3)=(81)/(8)m^(-4-(-6))n^(8-3)=(81)/(8)m^2n^5.`

Answer 2

Option B is correct.

`(81m^2n^5)/(8)` is equivalent to
`((3m^(-1)n^2)^4)/((2m^(-2)n)^3)`

Explanation:

Given expression:
`((3m^(-1)n^2)^4)/((2m^(-2)n)^3)`

Using exponents power:

• 
  `(ab)^n = a^nb^n`

• 
  `(a^n)^m = a^(nm)`

• 
  `a^m \cdot a^n = a^(m+n)`

Given:
`((3m^(-1)n^2)^4)/((2m^(-2)n)^3)`

Apply exponent power :

⇒
`(3^4 (m^(-1))^4(n^2)^4)/(2^3(m^(-2))^3 n^3)`

⇒
`(81 m^(-4)n^8)/(8m^(-6)n^3) = (81 m^(-4) \cdot m^6 n^8 \cdot n^(-3))/(8)`

⇒
`(81 m^(-4+6) n^(8-3))/(8) = (81 m^2 n^5)/(8) = (81m^2 n^5)/(8)`

Therefore, the expression which is equivalent to
`((3m^(-1)n^2)^4)/((2m^(-2)n)^3)` is,
`(81m^2 n^5)/(8)`