What is ((δk^{-ρ}l^p)/(l^p)+(1-δ)/(l^p))^{-1/ρ} ?

The solution to ((δk^{-ρ}l^p)/(l^p)+(1-δ)/(l^p))^{-1/ρ} is ((l^p)/(δl^pk^{-ρ)-δ+1})^{1/ρ}

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simplify ((δk^{-ρ}l^p)/(l^p)+(1-δ)/(l^p))^{-1/ρ}

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Combine the fractions

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

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

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

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

Combine same powers :

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = (\frac{x ^{a}}{y ^{b}})^{\frac{1}{m}}

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

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

(- 0.5)^{(- 0.5)}

- 9.72 e^{- 0.00006}

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

What is ((δk^{-ρ}l^p)/(l^p)+(1-δ)/(l^p))^{-1/ρ} ?
The solution to ((δk^{-ρ}l^p)/(l^p)+(1-δ)/(l^p))^{-1/ρ} is ((l^p)/(δl^pk^{-ρ)-δ+1})^{1/ρ}