Answer:
[tex]1. (5 \times 10^3) \times (9 \times 10^7) = 45 \times 10^{10}\\2. (7 \times 10^5) \div (2 \times 10^2) = 3.5 \times 10^3[/tex]
Step-by-step explanation:
Here, the given expressions are:
[tex]1. (5 \times 10^3) \times (9 \times 10^7)\\2. (7 \times 10^5) \div (2 \times 10^2)[/tex]
Now, the LAWS OF EXPONENTS state that:
[tex]1. a^ m \times a^n = a^{(m+n)}\\ 2. a^m \div a^n = a ^{(m-n)}[/tex]
Using above laws, we get:
[tex]1. (5 \times 10^3) \times (9 \times 10^7)\\= (5 \times 9 ) \times ( 10^7\times 10^3)\\= 45 \times (10^{(7+3)}) = 45 \times 10^{10}\\\implies (5 \times 10^3) \times (9 \times 10^7) = 45 \times 10^{10}[/tex]
[tex]2. (7 \times 10^5) \div (2 \times 10^2)\\= \frac{(7 \times 10^5)}{(2 \times 10^2)} = \frac{7}{2} \times\frac{10^5}{10^2} \\ =3.5 \times 10^{(5-2)} = 3.5 \times 10^3\\\implies(7 \times 10^5) \div (2 \times 10^2) = 3.5 \times 10^3[/tex]
