Expressions with Exponents: Free Course

About this course

Exponent notation expresses repeated multiplication compactly. This course develops exponent properties, negative powers and calculations in scientific notation. Study the complete public source playlist from Khan Academy in English, with all 21 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Apply product, quotient and power-of-power rules.
• Interpret negative exponents as reciprocals.
• Convert numbers to and from scientific notation.
• Multiply and divide quantities expressed in scientific notation.

Skills you’ll gain

• Exponent laws
• Negative powers
• Scientific notation
• Numerical scale

Course Overview

Products, quotients and powers of powers require different structural rules. Worked examples show how to combine them and how negative exponents relate to reciprocals. Scientific notation then separates a coefficient from a power of ten, making very large and very small quantities easier to compare and calculate with. Applications include distance, counts and a historical national-debt example; their role is practicing numerical representation rather than providing current measurements or financial information. Repeated scientific-notation demonstrations remain in the source sequence. Check the coefficient range after a calculation and explain the exponent change instead of treating normalization as a cosmetic formatting step.

How to study the course

• Videos 1–5: this part of the source list includes “Exponent properties 1” through “Multiplying three numbers in scientific notation (example)”. State the quantities and conditions before calculating. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 6–10: this part of the source list includes “Express a small number in scientific notation (example)” through “More negative exponent intuition”. Keep equivalent expressions or representations connected. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 11–15: this part of the source list includes “Introduction to negative exponents” through “U.S. national debt (scientific notation word problem)”. Check each operation with a small example before extending it. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 16–21: this part of the source list includes “Speed of light and distance from sun (scientific notation word problem)” through “Exponent properties involving products”. Explain a result in words as well as symbols. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits students, returning learners and anyone strengthening the specific mathematics named in the course. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort with the preceding arithmetic or algebra skills is useful. Keep paper, a pencil and a calculator when a lesson uses one. Grade-specific courses assume the learner’s earlier grade-level knowledge.

Put the lessons into practice

Choose one very large and one very small fictional quantity and write each in scientific notation. Multiply and divide them, normalizing the coefficient afterward. Simplify a separate expression containing products, quotients and negative powers, stating any restrictions on the base. Check one result by substituting an easy nonzero number.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.