Question

evaluate the expression.
$(6.4 \times 10^5) \div (4 \times 10^3)$
$? \times 10^{\square}$

Explanation:

Step1: Separate coefficients and powers of 10

We can rewrite the division of two numbers in scientific notation as the division of their coefficients and the division of their powers of 10. So, \((6.4\times10^{5})\div(4\times10^{3})=\frac{6.4}{4}\times\frac{10^{5}}{10^{3}}\)

Step2: Divide the coefficients

Calculate \(\frac{6.4}{4}\). \(6.4\div4 = 1.6\)

Step3: Divide the powers of 10

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

Step4: Combine the results

Multiply the results from Step 2 and Step 3. So, \(1.6\times10^{2}\)

Answer:

\(1.6\times10^{2}\)