3. a rectangular region of land in a state park has a length of 10,000 meters and a width of 4.8 × 10³…

Explanation:

Step1: Write the length in scientific notation

The length is (10000 = 1\times10^{4}) meters.

Step2: Use the formula for the area of a rectangle

The formula for the area of a rectangle is (A = l\times w), where (l) is the length and (w) is the width. Substitute (l = 1\times 10^{4}) and (w=4.8\times 10^{3}) into the formula: [ \begin{align*} A&=(1\times 10^{4})\times(4.8\times 10^{3})\ &=(1\times4.8)\times(10^{4}\times 10^{3}) \end{align*} ]

Step3: Apply the rule of exponents (a^{m}\times a^{n}=a^{m + n})

For the exponents, (10^{4}\times10^{3}=10^{4 + 3}=10^{7}), and (1\times4.8 = 4.8). So (A=4.8\times10^{7}) square - meters.

Answer:

(4.8\times 10^{7}) square meters.