What is ((5^{2(n+6)}*(25)^{-7+2n}))/(((125)^{2n))} ?

The solution to ((5^{2(n+6)}*(25)^{-7+2n}))/(((125)^{2n))} is 1/25

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simplify ((5^{2(n+6)}*(25)^{-7+2n}))/(((125)^{2n))}

simplify

\frac{( 5 ^{2 (n + 6)} \cdot ( 25 ) ^{- 7 + 2 n} )}{( ( 125 ) ^{2 n} )}

\frac{1}{25}

Decimal Notation

0.04

Solution steps

\frac{5 ^{2 (n + 6)} \cdot 2 5 ^{- 7 + 2 n}}{12 5 ^{2 n}}

Factor

12 5^{2 n} : 5^{6 n}

= \frac{5 ^{2 (n + 6)} \cdot 2 5 ^{- 7 + 2 n}}{5 ^{6 n}}

Simplify

\frac{5 ^{2 (n + 6)}}{5 ^{6 n}} : 5^{- 4 n + 12}

= 5^{- 4 n + 12} \cdot 2 5^{- 7 + 2 n}

Simplify

5^{- 4 n + 12} \cdot 2 5^{- 7 + 2 n} : \frac{1}{25}

= \frac{1}{25}

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What is ((5^{2(n+6)}*(25)^{-7+2n}))/(((125)^{2n))} ?
The solution to ((5^{2(n+6)}*(25)^{-7+2n}))/(((125)^{2n))} is 1/25