Question

va rog din suflet!! imi da nota!!​

Answer 1

sa ne amintim putin teoria ...

${a}^{m} \times {a}^{n} = {a}^{m + n} \\ {a}^{m} \div {a}^{n} = {a}^{m - n} \\ { {(a}^{m} )}^{n} = {a}^{m \times n} \\ {(a \times b)}^{n} = {a}^{n} \times {b}^{n} \\ { (\frac{a}{b} )}^{n} = \frac{ {a}^{n} }{ {b}^{n} }$

a)

$( {25}^{5} \times {5}^{6} \times {( {5}^{0}) }^{6} ) \div ( {5}^{10} \div {5}^{5} ) \times { ({5}^{3}) }^{3} \\ { ({5}^{2} )}^{5} \times {5}^{6} \times 1) \div {5}^{10 - 5} \times {5}^{3 \times 3} \\ {5}^{2 \times 5} \times {5}^{6} \div {5}^{5} \times {5}^{9} \\ {5}^{10 + 6} \div {5}^{5 + 9} = {5}^{16} \div {5}^{14} = {5}^{16 - 14} = {5}^{2} = 25$

b)

$( {( {7 ^{5} )}^{2}) }^{5} \div ( {7}^{23} \times {7}^{15} \times {7}^{0} \times 7 \times {7}^{9} ) \\ {7}^{5 \times 2 \times 5} \div ( {7}^{23} \times {7}^{15} \times 1 \times 7 \times {7}^{9} ) \\ {7}^{50} \div {7}^{23 + 15 + 1 + 9} = {7}^{50} \div {7}^{48} = {7}^{2} = 49$