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tensa zangetsu [6.8K]
3 years ago
6

Which expression is equivalent

Mathematics
2 answers:
gtnhenbr [62]3 years ago
4 0

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}

goldenfox [79]3 years ago
3 0

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.

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