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simplificar (4r^{71}s^8t^{69}u)(4r^{73}st^{57}u)

Solución

simplificar

(4 r^{71} s^{8} t^{69} u) (4 r^{73} s t^{57} u)

16 r^{144} s^{9} t^{126} u^{2}

Pasos de solución

(4 r^{71} s^{8} t^{69} u) (4 r^{73} s t^{57} u)

Aplicar las leyes de los exponentes:

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

4 \cdot 4 = 4^{1 + 1}

= r^{71} s^{8} t^{69} u \cdot 4^{1 + 1} r^{73} s t^{57} u

Sumar:

1 + 1 = 2

= r^{71} s^{8} t^{69} u \cdot 4^{2} r^{73} s t^{57} u

Aplicar las leyes de los exponentes:

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

r^{71} r^{73} = r^{71 + 73}

= s^{8} t^{69} u \cdot 4^{2} r^{71 + 73} s t^{57} u

Sumar:

71 + 73 = 144

= s^{8} t^{69} u \cdot 4^{2} r^{144} s t^{57} u

Aplicar las leyes de los exponentes:

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

s^{8} s = s^{8 + 1}

= t^{69} u \cdot 4^{2} r^{144} s^{8 + 1} t^{57} u

Sumar:

8 + 1 = 9

= t^{69} u \cdot 4^{2} r^{144} s^{9} t^{57} u

Aplicar las leyes de los exponentes:

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

t^{69} t^{57} = t^{69 + 57}

= u \cdot 4^{2} r^{144} s^{9} t^{69 + 57} u

Sumar:

69 + 57 = 126

= u \cdot 4^{2} r^{144} s^{9} t^{126} u

Aplicar las leyes de los exponentes:

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

uu = u^{1 + 1}

= 4^{2} r^{144} s^{9} t^{126} u^{1 + 1}

Sumar:

1 + 1 = 2

= 4^{2} r^{144} s^{9} t^{126} u^{2}

4^{2} = 16

= 16 r^{144} s^{9} t^{126} u^{2}

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