Question

Determine the product.
$800.5 \times (2 \times 10^6)$
A. $1.7 \times 10^7$
B. $1.601 \times 10^7$
C. $1.7 \times 10^9$
D. $1.601 \times 10^9$

Answer 1

Hint: Here we use the law of exponents, $x^a \times x^b = x^{a+b}$. When raising a base with a power to another power, keep the base the same and multiply the exponents.

Complete step-by-step answer:
We have to find the value of $800.5 \times (2 \times 10^6)$.
Opening the brackets, we get,
$800.5 \times (2 \times 10^6)=800.5 \times 2 \times 10^6$
Multiplying 800.5 and 2, we get,
$800.5 \times (2 \times 10^6)=1601 \times 10^6$
$\implies 800.5 \times (2 \times 10^6)=1.601 \times 10^6 \times 10^3$
Using law of exponents, we get,
$800.5 \times (2 \times 10^6)=1.601 \times 10^{6+3}$
$\implies 800.5 \times (2 \times 1^6)=1.601 \times 10^9$
Hence, option D is correct.

Note: In this type of questions, start by simplifying as much as you can by opening the brackets. After that by applying the law of exponents, one can obtain the required result.
Law of Exponents:
1. $x^a \times x^b = x^{a+b}$
2. $\dfrac{x^a}{x^b}=x^{a-b}$
3. $(x^a)^b =x^{ab}$