Algebra Fundamentals
Exponents and Radicals
Repeated multiplication made short: exponents and bases, negative bases, powers on the number line, squares, cubes and their roots, evaluating in order, working with radicals, the product, power and quotient rules, zero, negative and fraction exponents, prime factorization and scientific notation.
THE SYLLABUS
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Multiplication Patterns
Multiplying by the same number again and again makes a pattern of powers: each step is the step before times that number.
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Exponents
An exponent is a short way to write repeated multiplication: it counts how many times the base multiplies itself.
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Bases
The base is the number a power multiplies by; the exponent says how many times.
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Special Bases and Exponents
0 and 1 are special bases and 1 a special exponent: 0 to any positive power is 0, 1 to any power is 1, and any number to the power 1 is itself.
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Base 10
Our number system is built on powers of 10: 10ⁿ is a 1 followed by n zeros, and every number is a sum of digits times powers of 10.
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Level Check
Fifteen questions with no hints on exponent basics: missing bases, powers evaluated, next steps as products and powers, special bases, and a look back at linear patterns.
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II
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III
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IV
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V
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VI
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VII
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VIII
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IX
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X
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