Question

Multiply. (7.1×10^4)·(4.8×10^3)

A 3.408×107 ​
B 3.408×108
C 3.408×1012 ​
D 3.408×1013 ​

Answer 1

`Solution, \left(7.1* \:10^4\right)\left(4.8* \:10^3\right)=340800000`

`Steps:`

`\left(7.1* \:10^4\right)\left(4.8* \:10^3\right)`

`\mathrm{Remove\:parentheses}:\quad \left(a\right)=a, 7.1* \:10^4* \:4.8* \:10^3`

`\mathrm{Factor\:integer\:}10=2* \:5, 7.1\left(2* \:5\right)^4* \:4.8* \:10^3`

`\mathrm{Apply\:exponent\:rule}:\quad \left(ab\right)^c=a^cb^c, \left(2* \:5\right)^4=2^4* \:5^4, 7.1* \:2^4* \:5^4* \:4.8* \:10^3`

`\mathrm{Factor\:integer\:}10=2* \:5, 7.1* \:2^4* \:5^4* \:4.8\left(2* \:5\right)^3`

`\mathrm{Apply\:exponent\:rule}: \left(2* \:5\right)^3=2^3* \:5^3, 7.1* \:2^4* \:5^4* \:4.8* \:2^3* \:5^3`

`\mathrm{Apply\:exponent\:rule}:\quad \:a^b* \:a^c=a^(b+c), 2^4* \:2^3=\:2^(4+3)=\:2^7, 2^7* \:5^4* \:5^3* \:4.8* \:7.1`

`\mathrm{Apply\:exponent\:rule}: 5^4* \:5^3=\:5^(4+3)=\:5^7, 2^7* \:5^7* \:4.8* \:7.1`

`\mathrm{Multiply\:the\:numbers:}\:7.1* \:4.8=34.08, 2^7* \:5^7* \:34.08`

`2^7=128, 128* \:78125* \:34.08`

`5^7=78125, 128* \:78125* \:34.08`

`\mathrm{Multiply\:the\:numbers:}\:34.08* \:128* \:78125=340800000`

`\mathrm{The\:Correct\:Answer\:is\:B.\:3.408*10^8}`

`\mathrm{Hope\:This\:Helps!!!}`

`\mathrm{-Austint1414}`

Answer 2

the answer is B

3.408 to the 8th power