1. **Evaluate the expression** $6^{-2} - 4^{-2} - (-8)^{-2} - \frac{1}{36}$ step-byn step. 2. Recall that $a^{-n} = \frac{1}{a^n}$. 3. Calculate each term: $$ 6^{-2} = \frac{1}{6^2} = \frac{1}{36} $$ $$ 4^{-2} = \frac{1}{4^2} = \frac{1}{16} $$ $$ (-8)^{-2} = \frac{1}{(-8)^2} = \frac{1}{64} $$ 4. Substitute these values back into the expression: $$ \frac{1}{36} - \frac{1}{16} - \frac{1}{64} - \frac{1}{36} $$ 5. Combine like terms $\frac{1}{36} - \frac{1}{36} = 0$: $$ 0 - \frac{1}{16} - \frac{1}{64} = - \frac{1}{16} - \frac{1}{64} $$ 6. Find a common denominator for $\frac{1}{16}$ and $\frac{1}{64}$, which is 64: $$ - \frac{1}{16} = - \frac{4}{64} $$ 7. Now sum: $$ - \frac{4}{64} - \frac{1}{64} = - \frac{5}{64} $$ **Answer for first expression:** $-\frac{5}{64}$ --- **Scientific notation conversions:** 1. Convert $6.3 \times 10^3$ to digital number: $$ 6.3 \times 10^3 = 6.3 \times 1000 = 6300 $$ 2. Convert $23.7 \times 10^{-2}$ to digital number: $$ 23.7 \times 10^{-2} = 23.7 \times 0.01 = 0.237 $$ 3. Convert $52100$ to scientific notation: $$ 52100 = 5.21 \times 10^4 $$ 4. Convert $0.0035$ to scientific notation: $$ 0.0035 = 3.5 \times 10^{-3} $$