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/od-math-class-8-revision-term-1-2026/x181d712c63c19d29:week-2/x181d712c63c19d29:power-play/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/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/v/exponent-properties-involving-products 2023-05-08T07:03:29.632031759Z 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. Sal Khan video https://cdn.kastatic.org/googleusercontent/-PnQGCxScq8kPHAO5b0uYb9jKTqXC8YwDXZTcATH1r19L7Lj2EPqUfu7K1zdroefThOcYoOTAIMEBfs5Ph8YoHss 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/zM_p7tfWvLU.mp4/zM_p7tfWvLU.mp4 840 Power Play https://www.khanacademy.org/math/od-math-class-8-revision-term-1-2026/x181d712c63c19d29:week-2/x181d712c63c19d29:power-play/e/power-play-revision-exercise-1 2026-08-05T10:30:54.361523845Z Power Play - Revision Exercise 1 Power Play - Revision Exercise 1 Khan Academy exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/v/products-and-exponents-raised-to-an-exponent-properties 2023-07-28T22:13:00.844712665Z 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. Sal Khan video https://cdn.kastatic.org/googleusercontent/lBATfUWt09lNJ4yaaTFP-vM2x3MGy7JenLmkNXhq-K3VpHtrT7QAgK7m3A3v6WMbicLbmwWFN5mdA9TrFZrgRRwHGQ 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/SwqOrUWzDY8.mp4/SwqOrUWzDY8.mp4 358 Power Play https://www.khanacademy.org/math/od-math-class-8-revision-term-1-2026/x181d712c63c19d29:week-2/x181d712c63c19d29:power-play/v/the-zeroth-power-indian-accent 2025-06-25T06:06:22.643185463Z The zeroth power We consider two different ways to think about why a number raised to the zero power equals one: 1) if 2^3 = 1x2x2x2, then 2^0 = 1 times zero twos, which equals 1. 2) By following a pattern of decreasing an exponent by one by dividing by the base, we find that when we get to the 0 power, we end up dividing the base by itself, resulting in 1. Skyloom (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw The zeroth power We consider two different ways to think about why a number raised to the zero power equals one: 1) if 2^3 = 1x2x2x2, then 2^0 = 1 times zero twos, which equals 1. 2) By following a pattern of decreasing an exponent by one by dividing by the base, we find that when we get to the 0 power, we end up dividing the base by itself, resulting in 1. https://cdn.kastatic.org/ka-youtube-converted/GYZ-XM6th34.mp4/GYZ-XM6th34.mp4 232 Power Play https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/v/exponent-properties-involving-quotients 2021-07-02T09:35:36Z 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). Sal Khan video https://cdn.kastatic.org/googleusercontent/j5IyPzfCoWeyQz9F9c-oEqz9qHy7c5U-eC8UU7SI_HLofNW96mfX89bUpJASANOjRPa8sLv6RMa9rSHeA_sIll0 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/AR1uqNbjM5s.mp4/AR1uqNbjM5s.mp4 562 Power Play https://www.khanacademy.org/math/od-math-class-8-revision-term-1-2026/x181d712c63c19d29:week-2/x181d712c63c19d29:power-play/e/power-play-revision-exercise-2 2026-08-05T10:30:54.361523845Z Power Play - Revision Exercise 2 Power Play - Revision Exercise 2 Khan Academy exercise https://www.khanacademy.org/math/od-math-class-8-revision-term-1-2026/x181d712c63c19d29:week-2/x181d712c63c19d29:power-play/v/how-many-combinations 2026-01-16T10:30:37.091019215Z How Many Combinations In this video, we explore the idea of possible combinations using the fundamental principle of counting. You’ll learn how to figure out “how many ways” choices can be made by multiplying options step by step. With simple, everyday examples — like choosing shirts and trousers — we’ll show how combinations work in real life. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw How Many Combinations In this video, we explore the idea of possible combinations using the fundamental principle of counting. You’ll learn how to figure out “how many ways” choices can be made by multiplying options step by step. With simple, everyday examples — like choosing shirts and trousers — we’ll show how combinations work in real life. https://cdn.kastatic.org/ka-youtube-converted/XxSqgAaMQKQ.mp4/XxSqgAaMQKQ.mp4 376 Power Play https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-pos-neg-exponents/v/negative-exponents 2023-05-09T07:59:52.702064453Z 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. Sal Khan video https://cdn.kastatic.org/googleusercontent/lHpDDen3fL3H-T5RQ19AOObADW6YErcw5abMcjZu5gIH0MGYqnZXRbI4V9AbP26UsxcbidV-jjTZDB9Ki7rasko 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/JnpqlXN9Whw.mp4/JnpqlXN9Whw.mp4 434 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/od-math-class-8-revision-term-1-2026/x181d712c63c19d29:week-2/x181d712c63c19d29:power-play/e/power-play-revision-exercise-3 2026-08-05T10:30:54.361523845Z Power Play - Revision Exercise 3 Power Play - Revision Exercise 3 Khan Academy exercise