$9^{3.04} : 9^{2.04}$ is equal to

### Concept & Laws of Exponents When dividing exponential expressions with the same base, you subtract the exponent of the denominator from the exponent of the numerator. A ratio can be written as a fraction. $$ \frac{x^a}{x^b} = x^{a - b} $$ ### Step-by-Step Solution * **Given:** The ratio is $9^{3.04} : 9^{2.04}$. * **Rewrite as a fraction:** $\frac{9^{3.04}}{9^{2.04}}$ * **Apply the exponent rule:** Subtract the denominator's power from the numerator's power. $9^{3.04 - 2.04}$ * **Calculate the difference:** $3.04 - 2.04 = 1.00$. $9^1 = 9$ * **Format as a ratio:** The whole number $9$ can be written as a ratio over $1$. $9 : 1$ ### Exam Strategy & Shortcut Recognize immediately that the bases are identical ($9$). Simply subtract the decimals in your head: $3.04 - 2.04 = 1$. The result is $9^1$, which corresponds to the ratio $9 : 1$. ### Common Pitfall A common mistake is trying to calculate the actual immense values of $9^{3.04}$ and $9^{2.04}$ or incorrectly manipulating the decimal exponents, leading to a mismatched ratio. ### Final Answer Therefore, the correct answer is **$9 : 1$**.