Mathematics: Multiply (5 × 10^4)(7 × 10^3), express in scientific notation.

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Multiply (5 × 10^4)(7 × 10^3), express in scientific

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dontcareanyonemo

11.03.2022

How to get answer by Mimiwhatsup:

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=5\cdot \:10^4\cdot \:7\cdot \:10^3\\\mathrm{Factor\:integer\:}10=2\cdot \:5\\=5\left(2\cdot \:5\right)^4\cdot \:7\cdot \:10^3\\\mathrm{Apply\:exponent\:rule}:\quad \left(ab\right)^c=a^cb^c\\\left(2\cdot \:5\right)^4=2^4\cdot \:5^4\\=5\cdot \:2^4\cdot \:5^4\cdot \:7\cdot \:10^3\\\mathrm{Factor\:integer\:}10=2\cdot \:5\\=5\cdot \:2^4\cdot \:5^4\cdot \:7\left(2\cdot \:5\right)^3\\\mathrm{Apply\:exponent\:rule}:\quad \left(ab\right)^c=a^cb^c\\$

$\left(2\cdot \:5\right)^3=2^3\cdot \:5^3\\=5\cdot \:2^4\cdot \:5^4\cdot \:7\cdot \:2^3\cdot \:5^3\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\2^4\cdot \:2^3=\:2^{4+3}=\:2^7\\=2^7\cdot \:5^4\cdot \:5^3\cdot \:5\cdot \:7\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\5^4\cdot \:5^3\cdot \:5=\:5^{1+4+3}=\:5^8\\=5^8\cdot \:2^7\cdot \:7\\=5^8\cdot \:2^7\cdot \:7\\=5^8\cdot \:7\cdot \:128\\5^8=390625\\$

$\mathrm{Multiply\:the\:numbers:}\:7\cdot \:128\cdot \:390625=350000000$

Answer in Scientific Form and how to get it: Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

3.5 * 10^8

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Multiply (5 × 10^4)(7 × 10^3), express in scientific notation.

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