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 (0)})^{- 1}

3125

Solution steps

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

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- lo g_{10} (4.3) 1 0^{- 4}

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\frac{1}{2 π 4.32} \cdot e^{- 0.746}