Question

(5 × 10⁻³) · (7 × 10⁶)

Explanation:

Step1: Use commutative and associative properties

Rearrange the factors: \((5\times7)\times(10^{-3}\times10^{6})\)

Step2: Multiply the coefficients and use exponent rule

Multiply \(5\times7 = 35\), and for exponents \(a^m\times a^n=a^{m + n}\), so \(10^{-3}\times10^{6}=10^{-3 + 6}=10^{3}\)

Step3: Simplify the result

Now we have \(35\times10^{3}\), convert to proper scientific notation: \(3.5\times10^{4}\) (since \(35 = 3.5\times10^{1}\), then \(3.5\times10^{1}\times10^{3}=3.5\times10^{4}\))

Answer:

\(3.5\times10^{4}\)