Question

4.8x10^-4 / 8.0x10^-10

Answer 1

Given:

`(4.8*10^(-4))/(8.0*10^(-10))`

Separating the number and the exponents,

`\begin{gathered} (4.8)/(8.0)=0.6 \\ (10^(-4))/(10^(-10)),\text{ applying the quotient }law\text{ of exponent,} \\ (x^a)/(x^b)=x^(a-b) \\ \\ \text{Hence,} \\ (10^(-4))/(10^(-10))=10^(-4-(-10))=10^(-4+10)=10^6 \end{gathered}`

Combining both simplified number and exponent together,

`\begin{gathered} (4.8*10^(-4))/(8.0*10^(-10))=0.6*10^6 \\ 0.6*10^6,\text{ taking it to standard form,} \\ 0.6*10^6=6*10^(-1)*10^6 \\ \\ \text{Applying the product law of exponents,} \\ x^a* x^b=x^(a+b) \\ \text{Then,} \\ 6*10^(-1)*10^6=6*10^(-1+6)=6*10^5 \end{gathered}`

Therefore,

`(4.8*10^(-4))/(8.0*10^(-10))=6*10^5`