Question

(3.0x10^4)(8.9x10^-7)

Answer 1

0.0267

Explanation:

`\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)`

`10^4\cdot \:10^(-7)=\:10^(4-7)`

`\mathrm{Subtract\:the\:numbers:}\:4-7=-3`

`=3\cdot \:8.9\cdot \:10^(-3)`

`\mathrm{Apply\:exponent\:rule}:\quad \:a^(-b)=(1)/(a^b)`

`10^(-3)=(1)/(10^3)`

`\\=3\cdot \:8.9\cdot (1)/(10^3)`

`\mathrm{Multiply\:fractions}:\quad \:a\cdot (b)/(c)=(a\:\cdot \:b)/(c)`

`=8.9\cdot (1\cdot \:3)/(10^3)`

`(1 \cdot3)/(10^(3) ) =(3)/(1000)`

`=8.9\cdot (3)/(1000)`

`\mathrm{Multiply\:fractions}:\quad \:a\cdot (b)/(c)=(a\:\cdot \:b)/(c)`

`=(3\cdot \:8.9)/(1000)`

`\mathrm{Multiply\:the\:numbers:}\:3\cdot \:8.9=26.7`

`=(26.7)/(1000)`

`\mathrm{Divide\:the\:numbers:}\:(26.7)/(1000)=0.0267`

`=0.0267`