1. The problem asks to calculate $\left(9 \times 10^3\right)^2$ and express the answer in standard form. 2. The formula for squaring a product is $\left(ab\right)^2 = a^2 b^2$. 3. Applying this to our problem: $$\left(9 \times 10^3\right)^2 = 9^2 \times \left(10^3\right)^2$$ 4. Calculate each part: - $9^2 = 81$ - $\left(10^3\right)^2 = 10^{3 \times 2} = 10^6$ 5. Multiply the results: $$81 \times 10^6$$ 6. Expressing in standard form means writing the number as $a \times 10^n$ where $1 \leq a < 10$. 7. Since $81$ is not between 1 and 10, rewrite $81$ as $8.1 \times 10^1$: $$81 \times 10^6 = 8.1 \times 10^1 \times 10^6 = 8.1 \times 10^{1+6} = 8.1 \times 10^7$$ 8. Final answer in standard form: $$\boxed{8.1 \times 10^7}$$