What is ((5^n*5^3+5^n))/((5^n*5^{-1)*5^1)} ?

The solution to ((5^n*5^3+5^n))/((5^n*5^{-1)*5^1)} is 126

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simplify ((5^n5^3+5^n))/((5^n5^{-1)*5^1)}

simplify

\frac{( 5 ^{n} \cdot 5 ^{3} + 5 ^{n} )}{( 5 ^{n} \cdot 5 ^{- 1} \cdot 5 ^{1} )}

126

Solution steps

\frac{5 ^{n} \cdot 5 ^{3} + 5 ^{n}}{5 ^{n} \cdot 5 ^{- 1} \cdot 5 ^{1}}

Apply rule

a^{1} = a

5^{1} = 5

= \frac{5 ^{3} \cdot 5 ^{n} + 5 ^{n}}{5 ^{- 1} \cdot 5 \cdot 5 ^{n}}

5^{n} \cdot 5^{3} + 5^{n} = 5^{n + 3} + 5^{n}

= \frac{5 ^{n + 3} + 5 ^{n}}{5 ^{- 1} \cdot 5 \cdot 5 ^{n}}

5^{n} \cdot 5^{- 1} \cdot 5 = 5^{n}

= \frac{5 ^{n + 3} + 5 ^{n}}{5 ^{n}}

Factor

5^{n + 3} + 5^{n} : 126 \cdot 5^{n}

= \frac{126 \cdot 5 ^{n}}{5 ^{n}}

Cancel the common factor:

5^{n}

= 126

\frac{( 2 x + 3 \cdot 2 - 6 x + \frac{9}{4} x ^{2} - 99 - x ^{2} + 12 x - 3 )}{12 x}

p^{2} q^{2} - 64 a^{4}

(a^{5})^{6}

16 + 4 k^{2}

2 m^{3} + 26 m^{2} + 64 m + 40

What is ((5^n*5^3+5^n))/((5^n*5^{-1)*5^1)} ?
The solution to ((5^n*5^3+5^n))/((5^n*5^{-1)*5^1)} is 126