https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-exponents-and-order-of-operations/cc-6th-exponents/v/introduction-to-exponents 2023-05-07T10:59:10.383310828Z 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. Sal Khan video https://cdn.kastatic.org/googleusercontent/yo1n6SW3AG292oix4EzEgK4PwQTK-N8DeLIE-mEEm_vrXbPxbkW3u4qn8mHBToPDawcYUDS1uCjZy4465uCcSVVP 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/XZRQhkii0h0.mp4/XZRQhkii0h0.mp4 183 Exponents https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/x6b17ba59:powers-with-rational-bases/v/powers-of-1-and-1 2023-05-08T07:03:29.632031759Z 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. Sal Khan video https://cdn.kastatic.org/googleusercontent/4OCD6YX2YEBlDGqItYvuG7PEm66SOugJFqS7YWc4D_n64RH5vp9K4nrh0W3C0ZQJbInEj6O6CAOAn3JAC7S3PsP5 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/jYOfMszfzAQ.mp4/jYOfMszfzAQ.mp4 368 Exponents 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 Exponents 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 Exponents 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 Exponents https://www.khanacademy.org/math/math-nsdc-eng/x0a43a548b892fe12:exponents/x0a43a548b892fe12:properties-of-exponents/v/exponent-properties-4 2021-07-02T09:35:29Z Worked example: Exponent properties Use exponent properties to simplify a challenging expression. Sal Khan video https://cdn.kastatic.org/googleusercontent/MRAtKYVVl0AkyBzO_givRw-zyR3ABEUod-K5uxfA9Wa8uqaHETOmJUr6Z6r1OtNKDvg1TIngc6b-dHFo5M556rAJ Worked example: Exponent properties Use exponent properties to simplify a challenging expression. https://cdn.kastatic.org/ka-youtube-converted/X6zD3SoN3iY.mp4/X6zD3SoN3iY.mp4 187 Exponents 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 Exponents https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:exponent-properties-review/v/powers-of-products-and-quotients-integer-exponents 2022-10-06T11:39:29.972393653Z Powers of products & quotients (integer exponents) For any integers a and b and for any exponents n, (a⋅b)ⁿ=aⁿ⋅bⁿ and (a/b)ⁿ=aⁿ/bⁿ. These are worked examples for using these properties with integer exponents. video https://cdn.kastatic.org/ka_thumbnails_cache/4987c478-2b9d-41b7-99f8-00d76a5225e1_1280_720_base.png Powers of products & quotients (integer exponents) For any integers a and b and for any exponents n, (a⋅b)ⁿ=aⁿ⋅bⁿ and (a/b)ⁿ=aⁿ/bⁿ. These are worked examples for using these properties with integer exponents. https://cdn.kastatic.org/ka-youtube-converted/dC1ojsMi1yU.mp4/dC1ojsMi1yU.mp4 404 Exponents https://www.khanacademy.org/math/math-nsdc-eng/x0a43a548b892fe12:exponents/x0a43a548b892fe12:scientific-notation/v/scientific-notation-old 2021-07-02T09:35:34Z Introduction to scientific notation Introduction to scientific notation. An in-depth discussion about why and how scientific notation is used. Sal Khan video https://cdn.kastatic.org/googleusercontent/W2KLGS4tQaMllgQZhDKzO5OpPjnwuUhzAYvEVYUTLPqGFxa0t7RmBNYUggFdx7eoQHw-laoNjN_7cmEoZO_iTfk 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/trdbaV4TaAo.mp4/trdbaV4TaAo.mp4 1248 Exponents https://www.khanacademy.org/math/math-nsdc-eng/x0a43a548b892fe12:exponents/x0a43a548b892fe12:scientific-notation/v/scientific-notation-examples 2021-07-02T09:35:34Z Scientific notation examples More scientific notation examples Sal Khan video https://cdn.kastatic.org/googleusercontent/xhqZYrzEUYJ6pECzqQPefS3jy2KxXEW442ZYRg8sAuZ6dtmyYnzvPtju8GkSSxIH_GsyVrGcMLbV2ALjih8TvVU Scientific notation examples More scientific notation examples https://cdn.kastatic.org/ka-youtube-converted/0Dd-y_apbRw.mp4/0Dd-y_apbRw.mp4 769 Exponents https://www.khanacademy.org/math/revision-up-math-class-7/xad74f3b46242b79b:week-1-revision-up-math-class-7/xad74f3b46242b79b:exponents-revision-up-math-class-7/e/revision-exponents-up-math-class-7 2026-04-07T23:55:07.30621384Z Revision Exponents Practice problems for revision of Exponents. Satya Swaroop exercise