Question

Va rog ajutați-ma la rezolvarea unui ex. , va rog urgent

A)8^16 : (2 * 2^2 * 4^10)^2 -2^1 -2^0

B)(10^10-10^9):(10^9-10^8)

C) (2^2 * 2^4)^2:4^6-16^4:8^5:2^1:2^0

Answer 1

$a) {8}^{16} \div {(2 \times {2}^{2} \times {4}^{10} )}^{2} - {2}^{1} - {2}^{0}$

$= { ({2}^{3}) }^{16} \div {[2 \times {2}^{2} \times {( {2}^{2}) }^{10} ]}^{2} - 2 - 1$

$= {2}^{3 \times 16} \div {(2 \times {2}^{2} \times {2}^{2 \times 10} )}^{2} - 2 - 1$

$= {2}^{48} \div{ (2 \times {2}^{2} \times {2}^{20} )}^{2} - 2 - 1$

$= {2}^{48} \div { {(2}^{1 + 2 + 20}) }^{2} - 2 - 1$

$= {2}^{48} \div { ({2}^{23} )}^{2} - 2 - 1$

$= {2}^{48} \div {2}^{23 \times 2} - 2 - 1$

$= {2}^{48} \div {2}^{46} - 2 - 1$

$= {2}^{48 - 46} - 2 - 1$

$= {2}^{2} - 2 - 1$

$= 4 - 2 - 1$

$= 2 - 1$

$= 1$

$b)( {10}^{10} - {10}^{9} ) \div ( {10}^{9} - {10}^{8} )$

$= [ {10}^{9} (10 - 1)] \div [ {10}^{8} (10 - 1)]$

$= ( {10}^{9} \times 9) \div ( {10}^{8} \times 9)$

$= ( {10}^{9} \div {10}^{8} )(9 \div 9)$

$= {10}^{9 - 8} \times 1$

$= {10}^{1}$

$= 10$

$c) {( {2}^{2} \times {2}^{4} )}^{2} \div {4}^{6} - {16}^{4} \div {8}^{5} \div {2}^{1} \div {2}^{0}$

$= {( {2}^{2 + 4}) }^{2} \div {( {2}^{2}) }^{6} - { ({2}^{4} )}^{4} \div {( {2}^{3} )}^{5} \div 2 \div 1$

$= { ({2}^{6}) }^{2} \div {2}^{2 \times 6} - {2}^{4 \times 4} \div {2}^{3 \times 5} \div 2$

$= {2}^{6 \times 2} \div {2}^{12} - {2}^{16} \div {2}^{15} \div 2$

$= {2}^{12} \div {2}^{12} - {2}^{16 - 15 - 1}$

$= {2}^{12 - 12} - {2}^{1 - 1}$

$= {2}^{0} - {2}^{0}$

$= 1 - 1$

$= 0$