5^(2n-1) = 2 => 25^(3n-2)= ?

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5^(2n-1) = 2 => 25^(3n-2)= ?

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Answer 1 · 2017-05-06T09:12:42

$25^{3 n - 2} = \frac{8}{5}$ $25^(3n-2)=8/5$

Explanation:

$5^{2 n - 1} = 2 \Rightarrow 25^{3 n - 2 = ?}$ $5^(2n-1)=2" "rArr " "25^(3n-2=?$

$let us rearrange the the expression of 5^{2 n - 1} = 2$ $"let us rearrange the the expression of "5^(2n-1)=2$

$5^{2} n - 1 = 5^{2 n} \cdot 5^{- 1} = \frac{5^{2 n}}{5}$ $5^2n-1=5^(2n)*5^(-1)=5^(2n)/5$

$\frac{5^{2 n}}{5} = 2$ $5^(2n)/5=2$

$5^{2 n} = 10$ $5^(2n)=10$

$now ,let us rearrange the expression o f 25^{3 n - 2}$ $"now ,let us rearrange the expression o f "25^(3n-2$

$25^{3 n - 2} = 5^{2 (3 n - 2)} = 5^{6 n - 4} = 5^{6 n} \cdot 5^{- 4} = \frac{5^{6 n}}{5^{4}}$ $25^(3n-2)=5^(2(3n-2))=5^(6n-4)=5^(6n)*5^(-4)=5^(6n)/5^4$

$= \frac{5^{2 n} \cdot 5^{2 n} \cdot 5^{2 n}}{5^{4}} = \frac{10 \cdot 10 \cdot 10}{5^{4}} = \frac{1000}{625} = \frac{8}{5}$ $=(5^(2n)*5^(2n)*5^(2n))/5^4=(10*10*10)/5^4=1000/625=8/5$

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5^(2n-1) = 2 => 25^(3n-2)= ?

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