Question

1. (6.5 × 10⁻³)(4 × 10⁻²)

Explanation:

Step1: Multiply the coefficients

Multiply \( 6.5 \) and \( 4 \). So, \( 6.5\times4 = 26 \).

Step2: Multiply the powers of 10

Use the rule \( a^m\times a^n=a^{m + n} \) for \( 10^{-3}\times10^{-2} \). So, \( 10^{-3}\times10^{-2}=10^{-3+( - 2)}=10^{-5} \).

Step3: Combine the results

We have \( 26\times10^{-5} \). But in scientific notation, the coefficient should be between \( 1 \) and \( 10 \). So, rewrite \( 26 \) as \( 2.6\times10^{1} \). Then, \( 2.6\times10^{1}\times10^{-5}=2.6\times10^{1+( - 5)} = 2.6\times10^{-4} \).

Answer:

\( 2.6\times10^{-4} \)