Question

1. (9 × 10⁻⁴)(8.7 × 10¹⁰)

Explanation:

Step1: Use the commutative and associative properties of multiplication to group the coefficients and the powers of 10 together.

We can rewrite \((9\times10^{-4})(8.7\times10^{10})\) as \((9\times8.7)\times(10^{-4}\times10^{10})\).

Step2: Multiply the coefficients.

Calculate \(9\times8.7 = 78.3\).

Step3: Multiply the powers of 10 using the rule \(a^{m}\times a^{n}=a^{m + n}\).

For \(10^{-4}\times10^{10}\), we have \(10^{-4+10}=10^{6}\).

Step4: Combine the results from Step2 and Step3.

We get \(78.3\times10^{6}\). But in scientific notation, the coefficient should be between 1 and 10. So we rewrite \(78.3\) as \(7.83\times10^{1}\). Then, using the rule \(a^{m}\times a^{n}=a^{m + n}\) again, we have \(7.83\times10^{1}\times10^{6}=7.83\times10^{7}\).

Answer:

\(7.83\times10^{7}\)