Question

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

$\frac{7.5\times {10}^8}{2.5\times {10}^4}$

Short answer

The value of the given quotient$\frac{7.5\times {10}^8}{2.5\times {10}^4}$ in scientific notation is $3\times {10}^4$.

Step-by-step solution

Step 1. Evaluate the given quotient 7.5×1082.5×104.

The value of the given quotient $\frac{7.5\times {10}^8}{2.5\times {10}^4}$is:

$$\begin{gathered} \frac{7.5\times {10}^8}{2.5\times {10}^4}=\frac{7.5}{2.5}\times {10}^8\times {10}^{-4}\left(\because \frac{1}{a^m}=a^{-m}\right) \\ =3\times {10}^{8+\left(-4\right)}\left(\because a^m\times a^n=a^{m+n}\right) \\ =3\times {10}^{8-4} \\ =3\times {10}^4 \end{gathered}$$

Step 2. Express the result of the quotient 7.5×1082.5×104 in scientific notation.

The result of the given quotient$\frac{7.5\times {10}^8}{2.5\times {10}^4}$ in scientific notation is $3\times {10}^4$.