Powers and Exponent Laws
Exponent laws are shorthand for repeated patterns. x⁵ × x³ = x⁸ because five factors times three factors is eight factors total. Negative exponents express reciprocals (x⁻³ = 1/x³), and zero exponents always give 1. Scientific notation puts these laws to immediate use in handling very large and very small quantities.
What students explore
Exponent laws are shorthand for repeated patterns. x⁵ × x³ = x⁸ because five factors times three factors is eight factors total. Negative exponents express reciprocals (x⁻³ = 1/x³), and zero exponents always give 1. Scientific notation puts these laws to immediate use in handling very large and very small quantities.
Key ideas
Apply product, quotient, and power laws for exponents. Evaluate expressions with zero and negative exponents. Convert between scientific notation and standard form. Simplify expressions involving integer exponents.
Putting it together
Apply these ideas through worked examples, guided practice, and real-world problems.