Question

evaluate the expression.\\((8.4 \times 10^5) \div (2.1 \times 10^2)\\)\\(\boxed{?} \times 10^{\boxed{}}\\)

Explanation:

Step1: Separate the coefficients and the powers of 10

We can rewrite the division as the division of the coefficients and the division of the powers of 10. So, \((8.4\times10^{5})\div(2.1\times10^{2})=\frac{8.4}{2.1}\times\frac{10^{5}}{10^{2}}\)

Step2: Divide the coefficients

Calculate \(\frac{8.4}{2.1}\). Since \(8.4\div2.1 = 4\), the coefficient part is 4.

Step3: Divide the powers of 10

Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), for \(\frac{10^{5}}{10^{2}}\), we have \(10^{5-2}=10^{3}\)

Step4: Combine the results

Multiply the results from Step 2 and Step 3. So we get \(4\times10^{3}\)

Answer:

The first box is \(4\) and the second box is \(3\), so the expression is \(4\times10^{3}\)