1. **Simplify powers and expressions:** - Simplify expressions like $3^5 \cdot 3^{-9}$ and $(m^2)^{-6}$. - Apply exponent rules carefully, including negative exponents and zero exponents. 2. **Solve exponential equations:** - Solve equations such as $3^{x-3} = \frac{1}{27}$ and $2^{x-4} = \frac{1}{32}$. - Use properties of exponents to rewrite and solve for $x$. 3. **Identify and extend sequences:** - Determine if sequences are arithmetic or geometric. - Write the next three terms for sequences like $2, 6, 18, 54, ...$ and $-4, -9, -14, -19, -24, ...$. 4. **Find nth term and specific terms in sequences:** - Write formulas for the $n$th term of sequences. - Calculate terms such as $a_8$ for sequences like $3, 12, 48, 192, ...$. 5. **Analyze exponential growth and decay:** - Interpret functions like $y = 35,600(1.24)^x$ for population growth. - Calculate percent change and future values. 6. **Determine function types from tables:** - Decide if a table represents a linear or exponential function. - Identify growth or decay in exponential functions. 7. **Evaluate functions for given $x$ values:** - Compute values for functions such as $y = -2(5)^x$ at $x=6$. 8. **Graph exponential functions and find domain and range:** - Sketch graphs of functions like $f(x) = \frac{1}{2}3^x$. - Determine domain and range from the function and graph. 9. **Write exponential functions from word problems:** - Model situations like attendance growth or TV value depreciation. - Calculate future values using the functions. 10. **Solve more complex exponential equations:** - Solve equations involving multiple exponential terms, e.g., $3x 5^x = 5^{x-2}$. 11. **Evaluate roots and powers:** - Find real roots such as $ \sqrt[3]{8}$ and $ \sqrt[5]{-243}$. - Determine if solutions exist for roots of negative numbers with even indices. **Practice Test:** 1. Simplify $3^5 \cdot 3^{-9}$. 2. Solve $3^{x-3} = \frac{1}{27}$ for $x$. 3. Write the next three terms of the sequence $2, 6, 18, 54, ...$. 4. Find the formula for the $n$th term of the sequence $3, 12, 48, 192, ...$. 5. Calculate $a_8$ for the sequence in question 4. 6. Determine if the table with $x: 0,1,2,3$ and $y: 5,10,20,40$ represents linear or exponential growth. 7. Evaluate $y = -2(5)^x$ at $x=6$. 8. Write an exponential function for attendance starting at 34,500 increasing by 4.2% yearly. 9. Calculate attendance after 5 years using the function from question 8. 10. Solve $2^{-4x} = 16^{-2x+10}$ for $x$. 11. Find the real root of $x^3 = -27$. 12. Evaluate $ \sqrt[3]{8}$. 13. Determine if $\sqrt{-25}$ has a real solution. This practice test covers simplification, solving equations, sequences, function evaluation, graph interpretation, and root evaluation based on the provided review material.