Question

помогите плиз пример на фото​

Answer 1

1)

$( {6}^{4} ) {}^{4} \div (6 {}^{5} ) {}^{3} = 6 {}^{4 \times 4} \div {6}^{5 \times 3} = {6}^{16} \div {6}^{15} = \\ = 6 {}^{16 - 15} = 6$

2)

${8}^{3} \div 4 {}^{4} = ( {2}^{3} ) {}^{3} \div (2 {}^{2} ){}^{4} = {2}^{3\times 3} \div {2}^{2 \times 4} = \\ = 2{}^{9} \div {2}^{8} = {2}^{9 - 8} = 2$

3)

$\frac{ {7}^{14} \times ( {7}^{2}) {}^{3} }{( {7}^{3}) {}^{6} \times {7}^{2} } = \frac{7 {}^{14 + 2 \times 3} }{7 {}^{3 \times 6 + 2} } = \frac{ {7}^{14 + 6} }{ {7}^{18 + 2} } = \frac{ {7}^{20} }{ {7}^{20} } = 1$

4)

$\frac{ {25}^{3} \times {125}^{2} }{ {5}^{10} } = \frac{( {5}^{2} ) {}^{3} \times ( {5}^{3}) {}^{2} }{ {5}^{10} } = \frac{5 {}^{2 \times 3 + 3 \times 2} }{ {5}^{10} } = \\ = \frac{5 {}^{6 + 6} }{ {5}^{10} } = \frac{ {5}^{12} }{ {5}^{10} } = {5}^{2} = 25$