This course introduces powers as a short way to write repeated multiplication. You learn to read and write exponential form, learn the powers of the small numbers, and write a number as a power or as a product of prime powers. Then come the eleven laws of exponents, a few at a time: multiplying and dividing powers of the same base, powers of powers, products and quotients raised to a power, zero and negative exponents, powers of negative numbers, and equal powers, which let you solve for an unknown exponent. The course ends with mixed simplification and with standard form for very large and very small numbers.
Primary Years
Exponents (Level 1)
Exponential form and the eleven laws of exponents: multiplying and dividing powers, powers of powers, zero and negative exponents, negative bases, solving for an exponent, simplifying, and standard form.
- 8 lessons
Overview
Lessons
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Exponential form
Write repeated multiplication as a power, name the base and the exponent, learn the powers of small numbers, write a number as a power, and compare powers.
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Multiplying and dividing powers
Laws 1 and 2: to multiply powers of the same base add the exponents, and to divide them take the exponents away.
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Power of a power, product and quotient
Laws 3, 4 and 5: multiply the exponents for a power of a power, and join or split different bases that share the same power, with letters as well as numbers.
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Zero and negative exponents
Laws 6, 7 and 8: why a⁰ = 1, why a negative exponent means one over, and why a fraction with a negative exponent turns upside down.
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Powers of negative numbers
Laws 9 and 10: powers of −1 and of any negative number are positive for an even exponent and negative for an odd one, and why brackets matter.
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Equal powers and solving for the exponent
Law 11: equal powers of the same base have equal exponents. Write both sides as powers of one base and solve for the unknown exponent.
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Simplifying with the laws of exponents
All eleven laws in one table, each law used backwards, and mixed questions with brackets, negative exponents, fractions and fractional exponents worked step by step.
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Standard form
Write very large and very small numbers as k × 10ⁿ, change them back to ordinary form, multiply and divide in standard form, and compare such numbers.
Practice papers
Ten question papers that follow the lessons in order. Each has 20 questions for 50 marks (1 hour 30 minutes), with a key sheet and worked solutions.
MCQ tests
Ten tests of 25 multiple-choice questions (30 minutes each). Answer them on the page and check your score, or download the PDF with its key and solutions.
Class notes
Exponents (Level 1)
Typed from the teacher's handwritten class slides, 21 pages.
Download the notes (PDF, 897.6 KB)Exponents (Level 2)
Typed from the teacher's handwritten class slides, 16 pages.
Download the notes (PDF, 912.8 KB)