1. **Evaluate each expression with negative exponents:** **a)** $(-10)^{-2} = \frac{1}{(-10)^2} = \frac{1}{100}$ **b)** $(-4)^{-3} = \frac{1}{(-4)^3} = \frac{1}{-64} = -\frac{1}{64}$ **c)** $\left(\frac{1}{4}\right)^{-4} = 4^4 = 4 \times 4 \times 4 \times 4 = 256$ **d)** $\left(\frac{1}{3}\right)^{-3} = 3^3 = 3 \times 3 \times 3 = 27$ 2. **Write each expression as a single power and then evaluate:** **a)** $8^4 \times 8^{-2} = 8^{4 + (-2)} = 8^2 = 64$ **b)** $\frac{4^2}{4^3} = 4^{2 - 3} = 4^{-1} = \frac{1}{4}$ **c)** $\left(\frac{1}{3}\right)^{-5} \times \left(\frac{1}{3}\right)^7 = \left(\frac{1}{3}\right)^{-5 + 7} = \left(\frac{1}{3}\right)^2 = \frac{1}{9}$ **d)** $\frac{1}{(3^2)^2} = \frac{1}{3^{2 \times 2}} = \frac{1}{3^4} = \frac{1}{81}$ **e)** $\left(2^{-5}\right)^2 = 2^{-5 \times 2} = 2^{-10} = \frac{1}{1024}$ **f)** $\frac{5^4}{5^{-2}} = 5^{4 - (-2)} = 5^{6} = 15625$ **g)** $\left(\frac{1}{4}\right)^{-5} \times \left(\frac{1}{4}\right)^3 = \left(\frac{1}{4}\right)^{-5 + 3} = \left(\frac{1}{4}\right)^{-2} = 4^2 = 16$ **h)** $(-5)^4 \times (-5)^{-2} = (-5)^{4 + (-2)} = (-5)^2 = 25$ **i)** $\left(4^{-3}\right)^2 = 4^{-3 \times 2} = 4^{-6} = \frac{1}{4096}$ **j)** $\left(-\frac{1}{3}\right)^5 \times \left(-\frac{1}{3}\right)^{-7} = \left(-\frac{1}{3}\right)^{5 + (-7)} = \left(-\frac{1}{3}\right)^{-2} = \left(-3\right)^2 = 9$