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

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

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

simplify

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

\frac{15625 e ^{2}}{e ^{2} + 4}

Decimal Notation

10137.27569 \dots

Solution steps

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

Apply exponent rule:

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

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

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

= 5^{6} \cdot \frac{e ^{2}}{e ^{2} + 4}

Multiply fractions:

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

= \frac{e ^{2} \cdot 5 ^{6}}{e ^{2} + 4}

5^{6} = 15625

= \frac{15625 e ^{2}}{e ^{2} + 4}

(4 x 1 0^{- 6}) (2.5 x 1 0^{- 4})

- e^{x} e^{- x} 2 x (x + 1)^{2}

(2 a)^{2}

(2 x y) (x^{2} y^{3}) (2 y^{4})

- 2 x (0.5 x^{- 0.5})

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