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Popular Álgebra >

simplificar (21^635^380^3)/(15^414^930^2)

Solução

simplificar

\frac{2 1 ^{6} \cdot 3 5 ^{3} \cdot 8 0 ^{3}}{1 5 ^{4} \cdot 1 4 ^{9} \cdot 3 0 ^{2}}

Solução

2

Passos da solução

\frac{2 1 ^{6} \cdot 3 5 ^{3} \cdot 8 0 ^{3}}{1 5 ^{4} \cdot 1 4 ^{9} \cdot 3 0 ^{2}}

Fatorar

2 1^{6} : 3^{6} \cdot 7^{6}

= \frac{3 ^{6} \cdot 7 ^{6} \cdot 3 5 ^{3} \cdot 8 0 ^{3}}{1 5 ^{4} \cdot 1 4 ^{9} \cdot 3 0 ^{2}}

Fatorar

1 5^{4} : 3^{4} \cdot 5^{4}

= \frac{3 ^{6} \cdot 7 ^{6} \cdot 3 5 ^{3} \cdot 8 0 ^{3}}{3 ^{4} \cdot 5 ^{4} \cdot 1 4 ^{9} \cdot 3 0 ^{2}}

\frac{3 ^{6}}{3 ^{4}} = 3^{2}

= \frac{3 ^{2} \cdot 7 ^{6} \cdot 3 5 ^{3} \cdot 8 0 ^{3}}{5 ^{4} \cdot 1 4 ^{9} \cdot 3 0 ^{2}}

Fatorar

3 0^{2} : 3^{2} \cdot 1 0^{2}

= \frac{3 ^{2} \cdot 7 ^{6} \cdot 3 5 ^{3} \cdot 8 0 ^{3}}{5 ^{4} \cdot 1 4 ^{9} \cdot 3 ^{2} \cdot 1 0 ^{2}}

Eliminar o fator comum:

3^{2}

= \frac{7 ^{6} \cdot 3 5 ^{3} \cdot 8 0 ^{3}}{5 ^{4} \cdot 1 4 ^{9} \cdot 1 0 ^{2}}

Fatorar

1 4^{9} : 7^{9} \cdot 2^{9}

= \frac{7 ^{6} \cdot 3 5 ^{3} \cdot 8 0 ^{3}}{5 ^{4} \cdot 7 ^{9} \cdot 2 ^{9} \cdot 1 0 ^{2}}

\frac{7 ^{6}}{7 ^{9}} = \frac{1}{7 ^{3}}

= \frac{3 5 ^{3} \cdot 8 0 ^{3}}{5 ^{4} \cdot 7 ^{3} \cdot 2 ^{9} \cdot 1 0 ^{2}}

Fatorar

3 5^{3} : 5^{3} \cdot 7^{3}

= \frac{5 ^{3} \cdot 7 ^{3} \cdot 8 0 ^{3}}{5 ^{4} \cdot 7 ^{3} \cdot 2 ^{9} \cdot 1 0 ^{2}}

\frac{5 ^{3}}{5 ^{4}} = \frac{1}{5}

= \frac{7 ^{3} \cdot 8 0 ^{3}}{5 \cdot 7 ^{3} \cdot 2 ^{9} \cdot 1 0 ^{2}}

Eliminar o fator comum:

7^{3}

= \frac{8 0 ^{3}}{5 \cdot 2 ^{9} \cdot 1 0 ^{2}}

Fatorar

8 0^{3} : 5^{3} \cdot 1 6^{3}

= \frac{5 ^{3} \cdot 1 6 ^{3}}{5 \cdot 2 ^{9} \cdot 1 0 ^{2}}

\frac{5 ^{3}}{5} = 5^{2}

= \frac{5 ^{2} \cdot 1 6 ^{3}}{2 ^{9} \cdot 1 0 ^{2}}

Fatorar

1 0^{2} : 5^{2} \cdot 2^{2}

= \frac{5 ^{2} \cdot 1 6 ^{3}}{2 ^{9} \cdot 5 ^{2} \cdot 2 ^{2}}

Eliminar o fator comum:

5^{2}

= \frac{1 6 ^{3}}{2 ^{9} \cdot 2 ^{2}}

Fatorar

1 6^{3} : 2^{12}

= \frac{2 ^{12}}{2 ^{9} \cdot 2 ^{2}}

\frac{2 ^{12}}{2 ^{9}} = 2^{3}

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

Aplicar as propriedades dos expoentes:

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

= 2^{3 - 2}

Subtrair:

3 - 2 = 1

= 2^{1}

Aplicar as propriedades dos expoentes:

a^{1} = a

= 2

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