Question

Плиз быстрее надо срочно

Answer 1

$1) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ 128 \times {( \frac{1}{8}) }^{2} = 128 \times \frac{1}{64} = 2 \\ { ({6}^{3}) }^{2} \div {36}^{5} = {6}^{6} \div {( {6}^{2}) }^{5} = {6}^{6} \div {6}^{7} = {6}^{ - 1} = \frac{1}{6} \\ \\ 128 \times( \frac{1}{8} ) {}^{2} > { ({6}^{3} )}^{2} \div {6}^{5}$

$2) \: \: \: \: \: \frac{ {8}^{3} \times {2}^{5} }{ {16}^{4} } < 1 \frac{1}{8}$

$\frac{ {8}^{3} \times {2}^{5} }{ {16}^{4} } = \frac{ ({2 {}^{3} )}^{3} \times {2}^{5} }{( { {2}^{4}) }^{4} } = \frac{ {2}^{9} \times {2}^{5} }{ {2}^{16} } = \frac{ {2}^{14} }{ {2}^{16} } = \frac{1}{ {2}^{2} } = \frac{1}{4} = 0.25$

$1 \frac{1}{8} = 1.125[$

$3)13 \times {4}^{3} \div {2}^{3} > {10}^{2} \div {5}^{2} \div {2}^{3}$

${10}^{2} \div {5}^{2} \div {2}^{3} = {2}^{2} \times {5}^{2} \div {5}^{2} \div {2}^{3} = {2}^{ - 1} = \frac{1}{2} = 0.5$

$4) \frac{14 \times {3}^{2} \div {4}^{2} }{2 \times {3}^{3} } < \frac{ {21}^{3} \times 5 }{ {7}^{3} \times {3}^{4} }$

$\frac{14 \times {3}^{2} \div {4}^{2} }{2 \times {3}^{3} } = \frac{2 \times 7 \times {3}^{2} }{2 \times {3}^{3} \times {( {2}^{2}) }^{2} } = \frac{2 \times 7 \times {3}^{2} }{ {2}^{5} \times {3}^{3} } = \frac{7}{ {2}^{4} \times 3 } = \frac{7}{48}$

$\frac{ {21}^{3} \times 5 }{ {7}^{3} \times {3}^{4} } = \frac{ {7}^{3} \times {3}^{3} \times 5 }{ {7}^{3} \times {3}^{4} } = \frac{5}{3} = 1\frac{2}{3}$

$5)( - 0.5)^{3} \times 16 + 4 < {2}^{3} - 2.6$

$( - 0.5)^{3} \times 16 + 4 = - 0.125 \times 16 + 4 = - 2 + 4 = 2$

${2}^{3} - 2.6 = 8 - 2.6 = 5.4$

$6) {( - \frac{1}{4}) }^{4} \times 243 + {6}^{3} - 64 < {6}^{3} + ( { - 3)}^{2} - {2}^{5}$

$( - \frac{1}{3} {)}^{4} \times 243 + {6}^{3} - 64 = \frac{1}{81} \times 243 + 216 - 64 = 3 + 216 - 64 = 219 - 64 = 155$

${6}^{3} + ( { - 3)}^{2} - {2}^{5} = 216 + 9 - 32 = 225 - 32 = 193$

$7) {50}^{4} > {2}^{4} \div {5}^{ - 6}$

${50}^{4} = {25}^{4} \times {2}^{4} = { ({5}^{2} )}^{4} \times {2}^{4} = {5}^{8} \times {2}^{4}$

${2}^{4} \div {5}^{ - 6} = {2}^{4} \div \frac{1}{ {5}^{6} } = {2}^{4} \times {5}^{6}$

$8) {90}^{4} < {3}^{4} \div {10}^{ - 6}$

${90}^{4} = {9}^{4} \times {10}^{4} = { ({3}^{2} )}^{4} \times {10}^{4} = {3}^{8} \times {10}^{4}$

${3}^{4} \div {10}^{ - 6} = {3}^{4} \div \frac{1}{10 {}^{6} } = {3}^{4} \times {10}^{6}$