Question

Evaluate each product or quotient. Express the results in scientific notation.

$\left(2.13\times {10}^2\right)\left(3\times {10}^5\right)$

Short answer

The required expression is represented by $\mathbf{6}\mathbf{.39}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}$.

Step-by-step solution

Step 1. Write the numbers with exponents in separate parenthesis.

Split the numbers having exponents by using parenthesis.

$\left(2.13\times 3\right)\left({10}^2\times {10}^5\right)$

Step 2. Simplify the exponential terms.

Perform addition between the exponents having the same bases. Perform further simplification

$\left(6.39\right)\left({10}^{2+5}\right)=6.39\times {10}^7$

Step 3. Write the conclusion.

The obtained expression is in the form of $a\times {10}^n$means that$6.39\times {10}^7$ is the required notation.