[tex]Solution, \left(7.1\times \:10^4\right)\left(4.8\times \:10^3\right)=340800000[/tex]
[tex]Steps:[/tex]
[tex]\left(7.1\times \:10^4\right)\left(4.8\times \:10^3\right)[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a, 7.1\times \:10^4\times \:4.8\times \:10^3[/tex]
[tex]\mathrm{Factor\:integer\:}10=2\times \:5, 7.1\left(2\times \:5\right)^4\times \:4.8\times \:10^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(ab\right)^c=a^cb^c, \left(2\times \:5\right)^4=2^4\times \:5^4, 7.1\times \:2^4\times \:5^4\times \:4.8\times \:10^3[/tex]
[tex]\mathrm{Factor\:integer\:}10=2\times \:5, 7.1\times \:2^4\times \:5^4\times \:4.8\left(2\times \:5\right)^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}: \left(2\times \:5\right)^3=2^3\times \:5^3, 7.1\times \:2^4\times \:5^4\times \:4.8\times \:2^3\times \:5^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times \:a^c=a^{b+c}, 2^4\times \:2^3=\:2^{4+3}=\:2^7, 2^7\times \:5^4\times \:5^3\times \:4.8\times \:7.1[/tex]
[tex]\mathrm{Apply\:exponent\:rule}: 5^4\times \:5^3=\:5^{4+3}=\:5^7, 2^7\times \:5^7\times \:4.8\times \:7.1[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:7.1\times \:4.8=34.08, 2^7\times \:5^7\times \:34.08[/tex]
[tex]2^7=128, 128\times \:78125\times \:34.08[/tex]
[tex]5^7=78125, 128\times \:78125\times \:34.08[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:34.08\times \:128\times \:78125=340800000[/tex]
[tex]\mathrm{The\:Correct\:Answer\:is\:B.\:3.408*10^8}[/tex]
[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]
[tex]\mathrm{-Austint1414}[/tex]
