multiply. write your answer in scientific notation. (7.5 × 10²)(3.4 × 10⁻⁹)

Explanation:

Step1: Multiply the coefficients

Multiply (7.5) and (3.4). (7.5\times3.4 = 25.5)

Step2: Multiply the powers of 10

Use the rule (a^m\times a^n=a^{m + n}). Here (a = 10), (m=2) and (n=-9). (10^{2}\times10^{-9}=10^{2+( - 9)}=10^{-7})

Step3: Combine the results

((7.5\times10^{2})(3.4\times10^{-9})=(7.5\times3.4)\times(10^{2}\times10^{-9})) (=25.5\times10^{-7})

Step4: Adjust to scientific notation

Since in scientific notation (a\times10^{n}), (1\leqslant|a|\lt10). Rewrite (25.5\times10^{-7}) as (2.55\times10^{1}\times10^{-7}) Using (a^m\times a^n=a^{m + n}) again ((a = 10), (m = 1), (n=-7)) (2.55\times10^{1+( - 7)}=2.55\times10^{-6})

Answer:

(2.55\times10^{-6})