Question

Please can you give me the answer in standard form​​

Answer 1

Answer:

$1. (5 \times 10^3) \times (9 \times 10^7) = 45 \times 10^{10}\\2. (7 \times 10^5) \div (2 \times 10^2) = 3.5 \times 10^3$

Step-by-step explanation:

Here, the given expressions are:

$1. (5 \times 10^3) \times (9 \times 10^7)\\2. (7 \times 10^5) \div (2 \times 10^2)$

Now, the LAWS OF EXPONENTS state that:

$1. a^ m \times a^n = a^{(m+n)}\\ 2. a^m \div a^n = a ^{(m-n)}$

Using above laws, we get:

$1. (5 \times 10^3) \times (9 \times 10^7)\\= (5 \times 9 ) \times ( 10^7\times 10^3)\\= 45 \times (10^{(7+3)}) = 45 \times 10^{10}\\\implies (5 \times 10^3) \times (9 \times 10^7) = 45 \times 10^{10}$

$2. (7 \times 10^5) \div (2 \times 10^2)\\= \frac{(7 \times 10^5)}{(2 \times 10^2)} = \frac{7}{2} \times\frac{10^5}{10^2} \\ =3.5 \times 10^{(5-2)} = 3.5 \times 10^3\\\implies(7 \times 10^5) \div (2 \times 10^2) = 3.5 \times 10^3$