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Exponents are the mathematical equivalent of texting shortcuts like "TL;DR" — a compact way to express repeated multiplication without filling up an entire whiteboard. In this lesson covering Section 3.8 of Contemporary Mathematics, we break down every core exponent rule from the ground up, using vivid examples like astronomical distances, crossing out 14s in a giant fraction, and a delivery driver distributing exponents into parentheses. By the end, you'll see how each rule isn't an arbitrary law but a logical, inevitable consequence of the one before it. In this video: • Exponents as shorthand: why writing 8 multiplied by itself 19 times demands a better notation • Base vs. exponent: identifying the two parts of an expression like 7⁵ • Product rule: adding exponents when multiplying identical bases (9³ × 9⁵ = 9⁸), and why it fails for different bases like 5⁹ × 8⁴ • Quotient rule and the zero power rule: how crossing out 14s in a fraction leads to subtraction of exponents, and why 3⁰ must equal 1 • Distributive rule for products and fractions: the 'delivery driver' dropping an exponent of 4 onto both the 3 and the 7 in (3 × 7)⁴, and applying the same logic to (3/5)⁷ • Power rule: why (3⁶)⁴ becomes 3²⁴ by multiplying the exponents, traced back to the product rule • Negative exponent rule: using the 'elevator ticket' analogy to show that 4⁻² equals 1/4², and flattening fractions like 7³/13⁹ into a single line #OpenStax #Exponents #ContemporaryMathematics #CollegeMath #Algebra OpenStax Content adapted from "Contemporary Math", by OpenStax Licensed under CC BY 4.0. Content based on Web Version: Apr 23, 2026. Read the textbook online https://openstax.org/details/books/contemporary-mathematics Music first girl talking to me. by ikkun (ex. Barradeen) | https://soundcloud.com/ikkunwastaken Royalty Free Music by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en_US
Answer each question based on what was presented in the video lesson on exponents. No outside knowledge is required — all answers can be found in the video.
Apply the exponent rules from the video lesson to solve each problem. Show all steps and work from top to bottom — problems increase in difficulty.
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