Question

please solve it for me and give me full answer. I will thank your answer.​

Answer 1

5:) Express in power with base 2;

$\\ \sf (a) \: \: {64}^{ - 4}$

$\\\sf (b) \: \: ( {128}^{ - 3} ) \times ( {8}^{6} )$

$\\\sf (c) \: \: {32}^{ 4} \div {16}^{ - 5}$

$\\\sf (d) \: \: [(64)³×(-128)⁴]÷ {4}^{ - 5}$

Solution

$\\\\\sf (a) \: \: {64}^{ - 4}$

$\sf = { ({2}^{6}) }^{ - 4}$

$\sf = { ({2}^{6 \times - 4}) }$

$\underline{\sf = {2}^{ - 24}}$

$\sf (b) \: \: ( {128}^{ - 3} ) \times ( {8}^{6} )$

$\sf = ( {( {2}^{7}}) ^{ - 3} ) \times ( { {2}^{3}) }^{6}$

$\sf = {2}^{ - 21} \times {2}^{18}$

$\sf = {2}^{ - 21 + 18}$

$\underline{\sf = {2}^{ - 3}}$

$\sf (c) \: \: {32}^{ 4} \div {16}^{ - 5}$

$\sf = ({ {2}^{5} })^{ 4} \div ( { {2}^{4} })^{ - 5}$

$\sf = {2}^{20} \div {2}^{ - 20}$

$\sf = {2}^{20 - ( - 20)}$

$\sf = {2}^{20 + 20}$

$\underline{\sf = {2}^{40}}$

$\sf (d) \: \: [(64)³×(-128)⁴]÷ {4}^{ - 5}$

$\sf = [( {2}^{6} )³×( { - 2}^{7} )⁴]÷ ({ {2}^{2} })^{ - 5}$

$\sf = [ {2}^{18} × { - 2}^{28} ]÷ {2}^{ - 10}$

$\sf = [ {2}^{18} × { 2}^{28} ]÷ {2}^{ - 10}$

$\sf = [ {2}^{18 + 28} ]÷ {2}^{ - 10}$

$\sf = {2}^{46} ÷ {2}^{ - 10}$

$\sf = {2}^{46 - ( - 10)}$

$\sf = {2}^{46 + 10}$

$\underline{\sf = {2}^{56}}$

$\\ \sf (a) \: \: {64}^{ - 4}=\bf{2}^{ - 24}$

$\\\sf (b) \: \: ( {128}^{ - 3} ) \times ( {8}^{6} )=\bf{2}^{ - 3}$

$\\\sf (c) \: \: {32}^{ 4} \div {16}^{ - 5} = \bf {2}^{40}$

$\\\sf (d) \: \: [(64)³×(-128)⁴]÷ {4}^{ - 5}=\bf{2}^{56}$

Answer 2

all answers are attached in the attachment