What is 5^6(1+4e^{-2*0})^{-1} ?

The solution to 5^6(1+4e^{-2*0})^{-1} is 3125

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simplify 5^6(1+4e^{-2*0})^{-1}

simplify

5^{6} (1 + 4 e^{- 2 \cdot 0})^{- 1}

3125

Solution steps

5^{6} (1 + 4 e^{- 2 \cdot 0})^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= 5^{6} \cdot \frac{1}{( 4 e ^{- 2 \cdot 0} + 1 )}

1 + 4 e^{- 2 \cdot 0} = 5

= 5^{6} \cdot \frac{1}{5}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 5 ^{6}}{5}

Multiply:

1 \cdot 5^{6} = 5^{6}

= \frac{5 ^{6}}{5}

Cancel the common factor:

5

= 5^{5}

5^{5} = 3125

= 3125

\frac{3 ^{n}}{4 ^{n}}

(a - 3)^{2} (a + 3)^{2}

(2 \cdot 2) \cdot (2 \cdot 2)

4^{n} \cdot 3^{n}

0.4 a^{0} \cdot 0. 7^{- 4}