Exponentials Summary

Algebra 1 · Axiom Academy

SUMMARY Unit Summary: Exponentials A review of the exponent laws, special exponents, scientific notation, and the exponential functions that model growth and decay. Exponent rules are essential. Mastering them lets you simplify complex expressions and solve equations efficiently. Scientific notation is practical. It is the standard form for expressing very large or very small measurements in science and engineering. Exponential functions model change. When a quantity grows or decays at a rate proportional to its current size, an exponential function is the model. The base decides the behavior. A base b > 1 produces growth, while 0 < b < 1 produces decay. Core Concept Laws of Exponents When the bases match, multiplying adds exponents and dividing subtracts them. Raising a power to a power multiplies the exponents, and a power of a product distributes to each factor. When to use: simplifying any product, quotient, or nested power of like bases. Watch out for: the bases must be the same before you add or subtract exponents. Core Concept Special Exponents Any nonzero base raised to the zero power is 1 , and a negative exponent creates a reciprocal. Both fall straight out of the quotient rule applied to equal bases. When to use: rewriting reciprocals or clearing negative exponents. Watch out for: , which is not the same as -x^3 . Core Concept Scientific Notation

This is the written version of the interactive lesson above. See the full Algebra 1 course.