Students identify and record the zero and negative exponent rules (a^0 = 1 and a^{-n} = 1/a^n) and solve practice problems on the Negative & Zero Exponents activity page. In Activities 2 and 3, students apply the Product of Powers rule (a^m × a^n = a^{m+n}) and the Quotient of Powers rule (a^m ÷ a^n = a^{m-n}), including worked examples that add/subtract exponents and then convert negative results to reciprocals. Activities 4–6 require students to apply Power of a Power, Power of a Product (and Power of a Quotient in the answer key), and to produce exponent form and numerical answers on mixed-review problems.

Students calculate and interpret positive and negative integer exponents (e.g., using the calculator to evaluate 2^5 = 32 and entering negative exponents such as 2^(−3) to get 0.125 and relate it to 1/2^3). Students solve problems that require applying exponent rules, such as simplifying (2^3)^2 and multiplying like bases (3^4 · 3^2) on quizzes and activity pages. Real-world problems and exercises ask students to generate and evaluate exponential expressions (e.g., 3 × 2^4 and several problems finding squares, cubes, and their roots).

Students encounter tasks that require working with integer exponents on the Review Quiz and answer key: problems ask students to simplify 3^x × 3^4, evaluate (2)^4, use 2^n in an exponential growth formula, and compute side length and area expressions involving 2^3. The materials also include expressions with fractional/root notation (16^(1/3), √ expressions) and at least one reference to a negative exponent in an answer (e.g., 5^{-2} = 1/25), so students practice evaluating and simplifying exponential expressions in assessment items.

Students multiply and divide expressions in scientific notation and are instructed to add exponents when multiplying and subtract exponents when dividing (e.g., (3 × 10^4) × (6 × 10^3) and (6 × 10^8) ÷ (2 × 10^3)). Students convert negative exponents to standard decimals (e.g., 1.2 × 10^-4 → 0.00012) and convert between standard form and 10^n notation by moving the decimal point. Multiple activity pages and worked examples require students to perform these exponent operations with base 10 in a variety of problems and word contexts.

The Parent Plan explicitly lists the skill "Know and apply the properties of integer exponents to generate equivalent numerical expressions." Students convert decimals to scientific notation in Phase 1 (e.g., 0.0000042 → 4.2 × 10^-6) and work with given values in scientific notation (1.2 × 10^8 and 9.5 × 10^7) to compare and find differences. In Phase 3 students evaluate and use integer exponents in growth models (N = 2^t, compute 2^6 and 2^10, and compare 3^4).

The Parent Plan and student-facing introduction explicitly state that students should "use the rules for exponents (powers) to rewrite and simplify expressions" and even give the example 3^2 × 3^-5 = 3^-3 = 1/3^3 = 1/27. Multiple student problems require applying exponent properties: Problem 9 (5^3 × 5^2), Problem 10 (4^5 ÷ 4^3), Problem 11 (reciprocal of 3^-2), the bacteria growth problem using exponent addition, and other test items such as 3^4 × 3^2, 2^6 ÷ 2^3, and simplifying 4^-2. The answer keys convert negative exponents to fractional form (e.g., 4^-2 = 1/16) and demonstrate adding and subtracting exponents and combining bases in scientific notation.

The Parent Plan explicitly lists "Know and apply the properties of integer exponents to generate equivalent numerical expressions" as a targeted skill. In Task 3 students are given a fuel-cell energy amount written as 7 × 10^2 kWh and are instructed to convert this scientific-notation expression to a whole number (700 kWh). The Parent Plan and wrap-up also state students "perform operations with numbers expressed in scientific notation" and "use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities."

The Skills Review and its answer key include items that ask students to work with integer exponents: converting 5,600,000 to 5.6 × 10^6 and multiplying (3 × 10^7) × (2 × 10^3) with the result given as 6 × 10^6. The review also contains an exponent-simplification problem (answer key shows manipulating powers such as (2^3 × 2^2) ÷ 2^4 = 2^1 = 2), so students practice product/quotient rules for integer exponents and operations with powers of 10.

Students are asked to simplify multiplication of variables and are given the explicit hint x · x = x^2 in Activity 3, prompting them to write repeated factors as powers (e.g., problems and answer keys showing 3x^2y, 3a^2b). Several activities require students to multiply coefficients and combine like terms, producing expressions with exponents (Activity 3, Activity 4, and Activity 6 include x^2, a^2, q^2, etc.). Student tasks ask them to simplify products such as 3a · 3a · b · 2c into 18a^2bc, so students practice converting repeated multiplication into exponent notation in context.

Students complete Activity 3 "Exponent Escape Room," where they evaluate expressions that use exponent rules: 5^0, 2^3, 3^4 · 3^2 (product of powers with same base), (2^1)^2 (power of a power), and (4·5)^2 (power of a product). Students also answer a True/False item about 2^1 · 3^1 = 6^1 and must explain why bases must match to combine exponents, and they evaluate combined expressions such as (3^3)^2 + 3^3.

Students are asked to simplify expressions that require exponent rules: problem 8 asks them to simplify 6.9 × 10^2 (use of a power of 10), problem 9 asks them to simplify 5^1 × 5^2 (product rule for same base), and problem 10 asks them to simplify 8^4 ÷ 8^2 (quotient rule for same base). The answer key provides simplified results for these problems, indicating students are expected to generate equivalent numerical expressions using those properties.