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

Question 1

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

Question 2

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

Steps:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$\mathrm{-Austint1414}$

Question 3

the answer is B

3.408 to the 8th power

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