https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-vs-linear-growth/v/exponential-vs-linear-growth 2021-02-16T05:02:26Z Exponential vs. linear growth For constant increments in x, a linear growth would increase by a constant difference, and an exponential growth would increase by a constant ratio. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Exponential vs. linear growth For constant increments in x, a linear growth would increase by a constant difference, and an exponential growth would increase by a constant ratio. https://cdn.kastatic.org/ka-youtube-converted/_vlXdx-CqM0.mp4/_vlXdx-CqM0.mp4 185 Power Play https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/alg-exponential-vs-linear-growth/e/exponential-vs-linear-growth-warmup 2026-02-20T08:30:41.41782798Z Warmup: exponential vs. linear growth Make sure you have a good understanding of the difference between exponential and linear growth, before taking our exercise. Tomer Gal exercise https://www.khanacademy.org/math/od-math-class-8-new-book/x648dc020d7206462:power-play/x648dc020d7206462:experiencing-the-power-play/e/how-many-combinations 2026-01-14T04:19:20.590610231Z How many combinations In this exercise students learn about the Possible combinations - Through fundamental principle of counting Khan Academy exercise https://www.khanacademy.org/math/ka-math-class-7/x26f4f4b84655c15c:exponents-and-powers-ncert-new/x26f4f4b84655c15c:exponents/v/intro-to-exponents-indian-accent 2025-06-06T15:33:38.563209632Z Intro to exponents Exponents represent repeated multiplication, making numbers grow quickly. For example, 2 to the 3rd power means multiplying three 2's together, resulting in 8. This concept differs from multiplication, which is simply repeated addition. Understanding exponents is essential for mastering higher-level math. Skyloom (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Intro to exponents Exponents represent repeated multiplication, making numbers grow quickly. For example, 2 to the 3rd power means multiplying three 2's together, resulting in 8. This concept differs from multiplication, which is simply repeated addition. Understanding exponents is essential for mastering higher-level math. https://cdn.kastatic.org/ka-youtube-converted/WDXCfLVKqV0.mp4/WDXCfLVKqV0.mp4 137 Power Play https://www.khanacademy.org/math/ka-math-class-7/x26f4f4b84655c15c:exponents-and-powers-ncert-new/x26f4f4b84655c15c:exponents/v/1-and-1-to-different-powers-indian-accent 2025-06-06T15:33:38.563209632Z 1 and -1 to different powers Different exponents affect the value of a number: when raised to the power of zero, any number equals one; when raised to an even power, negative numbers yield positive results; and when raised to an odd power, negative numbers yield negative results. Skyloom (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw 1 and -1 to different powers Different exponents affect the value of a number: when raised to the power of zero, any number equals one; when raised to an even power, negative numbers yield positive results; and when raised to an odd power, negative numbers yield negative results. https://cdn.kastatic.org/ka-youtube-converted/zVDAQrlNNMM.mp4/zVDAQrlNNMM.mp4 333 Power Play https://www.khanacademy.org/math/class-7-tg/x476671d9fb9d8978:powers-and-exponents/x476671d9fb9d8978:untitled-305/e/exponents-2-a 2026-04-08T00:36:09.500768563Z Understanding exponents Basics of exponents ashish exercise https://www.khanacademy.org/math/8th-grade-illustrative-math/unit-7-exponents-and-scientific-notation/lesson-8-combining-bases/v/exponent-properties-with-products-indian-accent 2025-06-06T15:33:38.563209632Z Exponent properties with products To simplify expressions with exponents, there are a few properties that may help. One is that when two numbers with the same base are multiplied, the exponents can be added. Another is that when a number with an exponent is raised to another exponent, the exponents can be multiplied. Skyloom (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Exponent properties with products To simplify expressions with exponents, there are a few properties that may help. One is that when two numbers with the same base are multiplied, the exponents can be added. Another is that when a number with an exponent is raised to another exponent, the exponents can be multiplied. https://cdn.kastatic.org/ka-youtube-converted/pQ5hkjM-E1E.mp4/pQ5hkjM-E1E.mp4 762 Power Play https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/e/multiply-powers 2025-02-10T09:17:49.615690606Z Multiply powers Rewrite products of powers with the same base. For example, x²⋅x⁵ can be written as x⁷. Tome Gal exercise https://www.khanacademy.org/math/8th-grade-illustrative-math/unit-7-exponents-and-scientific-notation/lesson-6-what-about-other-bases/v/exponent-properties-with-parentheses-indian-accent 2025-06-06T15:33:38.563209632Z Exponent properties with parentheses Learn two exponent properties: (ab)^c = (a^c)*(b^c) and (a^b)^c = a ^ (b*c). See WHY they work and HOW to use them. In other words, multiplying two numbers, then raising the product to an exponent is the same as raising each number to that exponent and then multiplying. Raising a number to an exponent and then to another exponent equals raising the base to the product of the two exponents. Skyloom (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Exponent properties with parentheses Learn two exponent properties: (ab)^c = (a^c)*(b^c) and (a^b)^c = a ^ (b*c). See WHY they work and HOW to use them. In other words, multiplying two numbers, then raising the product to an exponent is the same as raising each number to that exponent and then multiplying. Raising a number to an exponent and then to another exponent equals raising the base to the product of the two exponents. https://cdn.kastatic.org/ka-youtube-converted/RUwsqBQmozA.mp4/RUwsqBQmozA.mp4 253 Power Play https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/e/powers-of-powers 2025-02-10T09:17:49.615690606Z Powers of powers Rewrite powers of powers. For example, (x²)⁵ can be written as x¹⁰. Tomer Gal exercise https://www.khanacademy.org/math/ncert-math-class-8-winter-bridge/x07a8c25cbfcc9660:week-1/x07a8c25cbfcc9660:exponents/v/exponent-properties-with-quotients-indian-accent 2025-06-06T15:33:38.563209632Z Exponent properties with quotients Learn how to simplify expressions like (5^6)/(5^2). Also learn how 1/(a^b) is the same as a^-b. Towards the end of the video, we practice simplifying more complex expressions like (25 * x * y^6)/(20 * y^5 * x^2). Skyloom (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Exponent properties with quotients Learn how to simplify expressions like (5^6)/(5^2). Also learn how 1/(a^b) is the same as a^-b. Towards the end of the video, we practice simplifying more complex expressions like (25 * x * y^6)/(20 * y^5 * x^2). https://cdn.kastatic.org/ka-youtube-converted/GVtO2QfTS04.mp4/GVtO2QfTS04.mp4 467 Power Play https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/e/divide-powers 2025-02-10T09:17:49.615690606Z Divide powers Rewrite quotients of powers with the same base. For example, (x⁵)/(x²) can be written as x³. Tomer Gal exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/e/powers-of-products-and-quotients 2026-02-11T18:54:16.791156652Z Powers of products & quotients Rewrite powers of products and quotients. For example, (3⁵⋅x³)² can be written as 3¹⁰⋅x⁶. Tomer Gal exercise https://www.khanacademy.org/math/8th-grade-illustrative-math/unit-7-exponents-and-scientific-notation/lesson-6-what-about-other-bases/v/negative-exponents-indian-accent 2025-06-06T15:33:38.563209632Z Negative exponents Negative exponents can be rewritten in two ways. Firstly, start with 1 and divide it by 2 the same number of times as the exponent. Secondly, take the reciprocal of the base and raise it to the positive exponent. Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Negative exponents Negative exponents can be rewritten in two ways. Firstly, start with 1 and divide it by 2 the same number of times as the exponent. Secondly, take the reciprocal of the base and raise it to the positive exponent. https://cdn.kastatic.org/ka-youtube-converted/G-v0wwQuGXA.mp4/G-v0wwQuGXA.mp4 434 Power Play https://www.khanacademy.org/math/revision-term-1-mh-math-class-7/x0bdc8a5f9d8ec377:week-3/x0bdc8a5f9d8ec377:indices/v/negative-exponent-intuition-indian-accent 2025-06-06T15:33:38.563209632Z Negative exponent intuition How do negative exponents work? Let's build our intuition about why a^(-b) = 1/(a^b) and how this definition keeps exponent rules consistent. Continue the pattern of decreasing exponents by dividing by 'a', and see how it extends to zero and negative powers. While we're at it, we'll see why a^0 =1. Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Negative exponent intuition How do negative exponents work? Let's build our intuition about why a^(-b) = 1/(a^b) and how this definition keeps exponent rules consistent. Continue the pattern of decreasing exponents by dividing by 'a', and see how it extends to zero and negative powers. While we're at it, we'll see why a^0 =1. https://cdn.kastatic.org/ka-youtube-converted/EdUl3AmZ_iM.mp4/EdUl3AmZ_iM.mp4 278 Power Play https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-pos-neg-exponents/e/exponents_2 2025-02-13T04:57:25.728250847Z Negative exponents Practice computing numbers raised to positive and negative exponents. Bases may be fractions. Jeff Ruberg exercise https://www.khanacademy.org/science/strengthened-shs-chemistry-1/x174677b2bfa4bea2:1st-quarter/x174677b2bfa4bea2:scientific-notations/v/introduction-to-scientific-notation-indian-accent 2025-06-06T15:33:38.563209632Z Introduction to scientific notation Introduction to scientific notation. An in-depth discussion about why and how scientific notation is used. Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Introduction to scientific notation Introduction to scientific notation. An in-depth discussion about why and how scientific notation is used. https://cdn.kastatic.org/ka-youtube-converted/yS-PXokT7tI.mp4/yS-PXokT7tI.mp4 1247 Power Play https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-scientific-notation/v/scientific-notation-i 2021-06-21T15:29:05Z Scientific notation example: 0.0000000003457 Can you imagine if you had to do calculations with very, very small numbers? How would you handle all those zeros to the right of the decimal? Thank goodness for scientific notation! Sal Khan video https://cdn.kastatic.org/googleusercontent/jFNy2bjU_nzHncfxuSOfq0fYkZSqu0vK80qD9I-SM1qhDJZoi3olmo1qRDVAQgd1Zv4sH2QfBtIRytExKFVD_JXt Scientific notation example: 0.0000000003457 Can you imagine if you had to do calculations with very, very small numbers? How would you handle all those zeros to the right of the decimal? Thank goodness for scientific notation! https://cdn.kastatic.org/ka-youtube-converted/6phoVfGKKec.mp4/6phoVfGKKec.mp4 252 Power Play https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-scientific-notation/v/scientific-notation 2023-04-30T21:01:15.828786566Z Scientific notation examples Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8. Created by Sal Khan and CK-12 Foundation. Sal Khan video https://cdn.kastatic.org/googleusercontent/oeA68O_Z8QW3ferd7a1lIjGLASQFOrElSOrLQTq2FkX1IwU3XqIN3rrU883ncM_qidLPCVW4L1IoWVi7OT2vzgZa Scientific notation examples Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8. Created by Sal Khan and CK-12 Foundation. https://cdn.kastatic.org/ka-youtube-converted/i6lfVUp5RW8.mp4/i6lfVUp5RW8.mp4 686 Power Play https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-scientific-notation/e/scientific_notation 2026-03-31T21:47:15.031073863Z Scientific notation Practice expressing numbers in scientific notation. Omar Rizwan exercise