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simplificar (2pir1/(pir^2))2(pir^2)

Solución

simplificar

(2 π r \cdot \frac{1}{π r ^{2}}) \cdot 2 (π r^{2})

4 π r

Pasos de solución

(2 π r \frac{1}{π r ^{2}}) \cdot 2 (π r^{2})

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

2 \cdot 2 = 2^{1 + 1}

= π r \frac{1}{π r ^{2}} \cdot 2^{1 + 1} π r^{2}

Sumar:

1 + 1 = 2

= π r \frac{1}{π r ^{2}} \cdot 2^{2} π r^{2}

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

r r^{2} = r^{1 + 2}

= π \frac{1}{π r ^{2}} \cdot 2^{2} π r^{1 + 2}

Sumar:

1 + 2 = 3

= π \frac{1}{π r ^{2}} \cdot 2^{2} π r^{3}

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

ππ = π^{1 + 1}

= \frac{1}{π r ^{2}} \cdot 2^{2} π^{1 + 1} r^{3}

Sumar:

1 + 1 = 2

= \frac{1}{π r ^{2}} \cdot 2^{2} π^{2} r^{3}

Multiplicar fracciones:

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

= \frac{1 \cdot 2 ^{2} π ^{2} r ^{3}}{π r ^{2}}

Multiplicar:

1 \cdot 2^{2} = 2^{2}

= \frac{2 ^{2} π ^{2} r ^{3}}{π r ^{2}}

Eliminar los terminos comunes:

π

= \frac{2 ^{2} π r ^{3}}{r ^{2}}

Aplicar las leyes de los exponentes:

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

\frac{r ^{3}}{r ^{2}} = r^{3 - 2}

= 2^{2} π r^{3 - 2}

Restar:

3 - 2 = 1

= 2^{2} π r

2^{2} = 4

= 4 π r

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