Question

multiply using scientific notation: \\((4 \cdot 10^3) (6 \cdot 10^2)\\) \\(2.4 \cdot 10^5\\) \\(24 \cdot 10^5\\) \\(24 \cdot 10^6\\) \\(2.4 \cdot 10^6\\)

Explanation:

Step1: Multiply coefficients and exponents

Multiply the coefficients \(4\) and \(6\): \(4\times6 = 24\).
Multiply the powers of \(10\) using \(a^m\times a^n=a^{m + n}\): \(10^3\times10^2=10^{3 + 2}=10^5\).
So, \((4\times10^3)(6\times10^2)=24\times10^5\).

Step2: Convert to proper scientific notation

Scientific notation requires the coefficient to be between \(1\) and \(10\).
Rewrite \(24\) as \(2.4\times10^1\).
Then, \(24\times10^5=(2.4\times10^1)\times10^5\).
Using \(a^m\times a^n=a^{m + n}\) again: \(10^1\times10^5 = 10^{1+5}=10^6\).
Thus, \(24\times10^5 = 2.4\times10^6\).

Answer:

\(2.4\cdot10^{6}\) (the last option, e.g., if the last option is \(2.4\cdot10^{6}\), then the answer is that option with its label)