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What is the value of the expression $34 x 3 y 3 z 3 ÷ 51 x y 2 z 3$ ?

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43 x 2 y

25 x 2 y

32 x 2 y

23 x 2 y

answer is D.

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Detailed Solution

The given expression is

34 x 3 y 3 z 3 ÷ 51 x y 2 z 3

.
Simplifying the given expression in numerator and denominator form, we get,

34 x 3 y 3 z 3 ÷ 51 x y 2 z 3 = 34 x 3 y 3 z 3 51 x y 2 z 3

Divide the monomial in the numerator by the monomial in the denominator using the formula

x m x n = x m − n,

34 x 3 y 3 z 3 51 x y 2 z 3 = 3451 × x 3 y 3 z 3 x y 2 z 3 = 23 x 2 y

Therefore, on solving

34 x 3 y 3 z 3 ÷ 51 x y 2 z 3,

the result is

23 x 2 y .

Hence, option 4 is correct.

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