Question

Which expression is equivalent

Answer 1

Answer:

Option  B is correct.

$\frac{81m^2n^5}{8}$ is equivalent to $\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}$

Step-by-step explanation:

Given expression: $\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}$

Using exponents power:

• $(ab)^n = a^nb^n$

• $(a^n)^m = a^{nm}$

• $a^m \cdot a^n = a^{m+n}$

Given: $\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}$

Apply exponent power :

⇒ $\frac{3^4 (m^{-1})^4(n^2)^4}{2^3(m^{-2})^3 n^3}$

⇒ $\frac{81 m^{-4}n^8}{8m^{-6}n^3} = \frac{81 m^{-4} \cdot m^6 n^8 \cdot n^{-3}}{8}$

⇒$\frac{81 m^{-4+6} n^{8-3}}{8} = \frac{81 m^2 n^5}{8} = \frac{81m^2 n^5}{8}$

Therefore, the expression which is equivalent to  $\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}$ is,  $\frac{81m^2 n^5}{8}$

Answer 2

Answer:

Correct choice is B

Step-by-step explanation:

Consider expression

$\dfrac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}.$

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,

$\dfrac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}=\dfrac{81m^{-4}n^8}{8m^{-6}n^3}=\dfrac{81}{8}m^{-4-(-6)}n^{8-3}=\dfrac{81}{8}m^2n^5.$