Question

ayuda plis con el punto 4

110965dbed769b715254ce35fd96621e.pdf

Answer 1

Hola!

Explicación paso a paso:

∆) Solución:

a)

$( {14}^{2} \times {14}^{3} ) \div 14 \\ \\ = \frac{( {14}^{2} \times {14}^{3}) }{ {14}^{1} } = \frac{ {14}^{2 + 3} }{ {14}^{1} } \\ = \frac{ {14}^{5} }{ {14}^{1} } = {14}^{5 - 1} = {14}^{4} = 38 \: 416$

b)

${8}^{4} \times {8}^{2} = {8}^{4 + 2} = {8}^{6} = 262 \: 144$

c)

${2}^{8} \times {2}^{2} \times 2 = {2}^{8} \times {2}^{2} \times {2}^{1} \\ = {2}^{8 + 2 + 1} = {2}^{11} = 2 \: 048$

d)

${5}^{3} \times {5}^{12} \div {5}^{9} = \frac{ {5}^{3} \times {5}^{12} }{ {5}^{9} } = \frac{ {5}^{3 + 12} }{ {5}^{9} } \\ = \frac{ {5}^{15} }{ {5}^{9} } = {5}^{15 - 9} = {5}^{6} = 15 \: 625$

e)

$( {7}^{15} \div {7}^{13} ) \div {7}^{2} = ( \frac{ {7}^{15} }{ {7}^{13} } ) \div {7}^{2} \\ = ({7}^{15 - 13} ) \div {7}^{2} = ( {7}^{2} ) \div {7}^{2} = \frac{ {7}^{2} }{ {7}^{2} } = {7}^{2 - 2} = {7}^{0} = 1$

f)

${ ({3}^{4} )}^{2} \times 3 \div {3}^{5} = {3}^{4 \times 2} \times 3 \div {3}^{5} \\ = {3}^{8} \times {3}^{1} \div {3}^{5} = {3}^{8 + 1} \div {3}^{5} = {3}^{9} \div {3}^{5} \\ = \frac{ {3}^{9} }{ {3}^{5} } = {3}^{9 - 5} = {3}^{4} = 81$

G)

${(3 \times 6)}^{8} \div {3}^{5} = {(3 \times 3 \times 2)}^{8} \div {3}^{5} \\ = {( {3}^{2} \times 2)}^{8} \div {3}^{5} = {3}^{2 \times 8} \times {2}^{1 \times 8} \div {3}^{5} \\ = {3}^{16} \times {2}^{8} \div {3}^{5} = \frac{ {3}^{16} \times {2}^{8} }{ {3}^{5} } = {3}^{16 - 5} \times {2}^{8} \\ = {3}^{11} \times {2}^{8} = 177 \: 147 \times 256 = \: 45 \: 349 \: 632$

h)

${( {9}^{7} )}^{0} \times 9 = 1 \times 9 = 9$

I)

$\frac{ {( {11}^{5} )}^{4} \times {( {11}^{3}) }^{6} }{ {11}^{11} } = \frac{ {11}^{5 \times 4} \times {11}^{3 \times 6} }{ {11}^{11} } = \frac{ {11}^{20} \times {11}^{18} }{ {11}^{11} } \\ = \frac{ {11}^{20 + 18} }{ {11}^{11} } = \frac{ {11}^{38} }{ {11}^{11} } = {11}^{38 - 11} = {11}^{27}$

j)

$\frac{{( {13}^{6}) }^{2} \times { ({ ({13}^{3} )}^{4}) }^{2} }{ {13}^{10} } = \frac{ {13}^{6 \times 2} \times {13}^{3 \times 4 \times 2} }{ {13}^{10} } \\ = \frac{ {13}^{12} \times {13}^{24} }{ {13}^{10} } = \frac{ {13}^{12 + 24} }{ {13}^{10} } = \frac{ {13}^{36} }{ {13}^{10} } = {13}^{36 - 10} = {13}^{26}$