How do you simplify ${(\frac{2 p^{- 2} q^{3}}{4 p^{8} q^{- 5}})}^{- 5}$ $(\frac { 2p ^ { - 2} q ^ { 3} } { 4p ^ { 8} q ^ { - 5} } ) ^ { - 5}$ ?

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Answer 1 · 2017-11-27T16:12:39

$\frac{32 p^{50}}{q^{40}}$ $(32p^50)/q^40$

${(\frac{2 p^{- 2} q^{3}}{4 p^{8} q^{- 5}})}^{- 5}$ $((2p^-2q^3)/(4p^8q^-5))^-5$

First use the exponent rule ${(x^{a})}^{b} = x^{a b}$ $(x^a)^b = x^(ab)$ .

$\frac{2^{- 5} p^{10} q^{- 15}}{4^{- 5} p^{- 40} q^{25}}$ $(2^-5p^10q^-15)/(4^-5p^-40q^25)$

Use the exponent rule $x^{- a} = \frac{1}{x^{a}}$ $x^-a = 1/x^a$ and $\frac{1}{x^{- b}} = x^{b}$ $1/x^-b = x^b$ .

$\frac{4^{5} p^{10} p^{40}}{2^{5} q^{25} q^{15}}$ $(4^5p^10p^40)/(2^5q^25q^15)$

Use the exponent rule $x^{a} \cdot x^{b} = x^{a + b}$ $x^a *x^b= x^(a+b)$

$\frac{4^{5} p^{50}}{2^{5} q^{40}}$ $(4^5p^50)/(2^5q^40)$

Simplify the coefficients.

$\frac{1024 p^{50}}{32 q^{40}}$ $(1024p^50)/(32q^40)$

Divide the coefficients.

$\frac{32 p^{50}}{q^{40}}$ $(32p^50)/q^40$

How do you simplify (2p−2q34p8q−5)−5(\frac { 2p ^ { - 2} q ^ { 3} } { 4p ^ { 8} q ^ { - 5} } ) ^ { - 5}?