Question

ly.
× 10⁵)(8 × 10²)
× 10¹³ 4 × 10⁷ 4 × 10⁸ 4 × 10
submit

Explanation:

Step1: Assume the first number is \(5\times10^5\) (since part is missing, common problem: \((5\times10^5)(8\times10^2)\) correction: Wait, maybe it's \((5\times10^5)(8\times10^2)\)? No, wait, the options have 4, so maybe the first number is \(5\times10^5\) and second? Wait, no, let's check standard scientific notation multiplication. Wait, maybe the first term is \(5\times10^5\) and second is \(8\times10^2\)? No, the options have 4, so maybe the first number is \(5\times10^5\) and actually, maybe a typo, let's assume the problem is \((5\times10^5)(8\times10^2)\)? No, wait, the options have 4, so maybe the first number is \(0.5\times10^6\) (which is \(5\times10^5\)) and second is \(8\times10^2\)? Wait, no, let's do scientific notation multiplication: \((a\times10^m)(b\times10^n)=ab\times10^{m + n}\). If the first term is \(5\times10^5\) and second is \(8\times10^2\), then \(5\times8 = 40\), \(10^{5+2}=10^7\), so \(40\times10^7 = 4\times10^8\) (since \(40 = 4\times10^1\), so \(4\times10^1\times10^7=4\times10^8\)). Wait, maybe the first number is \(5\times10^5\) and second is \(8\times10^2\), but the first number in the problem is cut off, but the options include \(4\times10^8\). Let's proceed with correct steps:

Wait, let's assume the problem is \((5\times10^5)(8\times10^2)\) – no, 5×8=40, 10^5×10^2=10^7, so 40×10^7=4×10^8 (because 40=4×10^1, so 4×10^1×10^7=4×10^8). So the correct option should be \(4\times10^8\).

Step2: Multiply coefficients and exponents.

Coefficients: Let's say the first coefficient is 5 (assuming the missing part is 5×10^5) and second is 8. 5×8=40. Exponents: 10^5×10^2=10^(5+2)=10^7. Then 40×10^7=4×10^8 (since 40=4×10^1, so 4×10^1×10^7=4×10^(1+7)=4×10^8).

Answer:

\(4 \times 10^8\) (the third option, labeled \(4 \times 10^8\))