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

The solution to 5^6(1+4e^{-2(2)})^{-1} is (15625e^4)/(e^4+4)

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

simplify

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

\frac{15625 e ^{4}}{e ^{4} + 4}

Decimal Notation

14558.41342 \dots

Solution steps

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

Apply exponent rule:

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

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

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

= 5^{6} \cdot \frac{e ^{4}}{e ^{4} + 4}

Multiply fractions:

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

= \frac{e ^{4} \cdot 5 ^{6}}{e ^{4} + 4}

5^{6} = 15625

= \frac{15625 e ^{4}}{e ^{4} + 4}

(\frac{δ k ^{- ρ} l ^{p}}{l ^{p}} + \frac{1 - δ}{l ^{p}})^{- \frac{1}{ρ}}

(2 \cdot 3.14 \cdot 580000)^{2} \cdot 2.8 \cdot 1 0^{- 9}

(- 0.5)^{(- 0.5)}

What is 5^6(1+4e^{-2(2)})^{-1} ?
The solution to 5^6(1+4e^{-2(2)})^{-1} is (15625e^4)/(e^4+4)