To solve the expression and express it in scientific notation, let's break down the operation step-by-step:
1. Write down the given values:
[tex]\[
\text{numerator} = 9.0 \times 10^{-5}
\][/tex]
[tex]\[
\text{denominator} = 2.0 \times 10^{-8}
\][/tex]
2. Perform the division of the coefficients:
[tex]\[
\frac{9.0}{2.0} = 4.5
\][/tex]
3. Handle the powers of ten separately:
Use the property of exponents:
[tex]\[
\frac{10^{-5}}{10^{-8}} = 10^{-5 - (-8)} = 10^{-5 + 8} = 10^{3}
\][/tex]
4. Combine the results of the coefficients and the powers of ten:
[tex]\[
\frac{9.0 \times 10^{-5}}{2.0 \times 10^{-8}} = 4.5 \times 10^{3}
\][/tex]
5. Express the answer correctly in scientific notation:
The coefficient is [tex]\( 4.5 \)[/tex] and the exponent is [tex]\( 3 \)[/tex].
Therefore, the final answer is:
[tex]\[
\frac{9.0 \times 10^{-5}}{2.0 \times 10^{-8}} = \boxed{4.5} \times 10^{\boxed{3}}
\][/tex]
