Question

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

$\frac{6.6\times {10}^5}{2\times {10}^{-3}}$

Short answer

The value of the given quotient$\frac{6.6\times {10}^5}{2\times {10}^{-3}}$ in scientific notation is $3.3\times {10}^8$.

Step-by-step solution

Step 1. Evaluate the given quotient 6.6×1052×10−3.

The value of the given quotient $\frac{6.6\times {10}^5}{2\times {10}^{-3}}$is:

$$\begin{gathered} \frac{6.6\times {10}^5}{2\times {10}^{-3}}=\frac{6.6}{2}\times {10}^5\times {10}^{-\left(-3\right)}\left(\because \frac{1}{a^m}=a^{-m}\right) \\ =3.3\times {10}^5\times {10}^3 \\ =3.3\times {10}^{5+3}\left(\because a^m\times a^n=a^{m+n}\right) \\ =3.3\times {10}^8 \end{gathered}$$

Step 2. Express the result of the quotient 6.6×1052×10−3 in scientific notation.

The result of the given quotient$\frac{6.6\times {10}^5}{2\times {10}^{-3}}$ in scientific notation is $3.3\times {10}^8$.