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 Laws of exponents 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/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 Laws of exponents 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/up-class-9-bridge/x27a9f6658c8b5c27:number-system-and-exponents/x27a9f6658c8b5c27:untitled-15/v/multiplying-dividing-powers-integer-exponents--indian-accent 2025-06-09T09:58:43.937294419Z Multiplying & dividing powers (integer exponents) For any base a and any integer exponents n and m, aⁿ⋅aᵐ=aⁿ⁺ᵐ. For any nonzero base, aⁿ/aᵐ=aⁿ⁻ᵐ. These are worked examples for using these properties with integer exponents. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (add course link here) Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Multiplying & dividing powers (integer exponents) For any base a and any integer exponents n and m, aⁿ⋅aᵐ=aⁿ⁺ᵐ. For any nonzero base, aⁿ/aᵐ=aⁿ⁻ᵐ. These are worked examples for using these properties with integer exponents. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (add course link here) Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by https://cdn.kastatic.org/ka-youtube-converted/sSfv-x0UB3k.mp4/sSfv-x0UB3k.mp4 264 Laws of exponents https://www.khanacademy.org/math/uk-math-class-8/x40384ea0c3a0cfc9:exponents-and-power-ncert-new/x40384ea0c3a0cfc9:laws-of-exponents/e/evaluating-powers-of-powers 2025-08-20T06:36:47.846225857Z Evaluating powers of powers This exercise is curated to have simple widgets for new ncert and the problems are replicated from exercise named powers of powers Devashish Phadnis exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:exponent-properties-review/e/powers-of-powers-int-exp 2026-02-09T16:46:38.21172116Z Powers of products & quotients (integer exponents) Rewrite powers where the base includes more powers, and the exponents may be negative. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:exponent-properties-review/e/properties-of-integer-exponents 2023-12-12T00:32:03.629852833Z Properties of exponents challenge (integer exponents) A quiz that covers all exponent properties using integer exponents. Tomer Gal exercise https://www.khanacademy.org/math/ka-math-class-7/x26f4f4b84655c15c:exponents-and-powers-ncert-new/x26f4f4b84655c15c:exponents/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 Laws of exponents https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/x6b17ba59:powers-with-rational-bases/v/exponents-with-negative-bases 2021-06-28T22:10:43Z Exponents with negative bases Learn to what we know about negative numbers to determine how negative bases with exponents are affected and what patterns develop. Also learn how order of operations affect the pattern. Sal Khan video https://cdn.kastatic.org/googleusercontent/a2tKMz7K_pqMVl5ES3myFKpudTzatti6A_9XmyQTIjF4JwVmtMjck4aIqa3npF_ynimwPfgJ9g1meLlSKb4K4RtfwA Exponents with negative bases Learn to what we know about negative numbers to determine how negative bases with exponents are affected and what patterns develop. Also learn how order of operations affect the pattern. https://cdn.kastatic.org/ka-youtube-converted/vEZea0EThus.mp4/vEZea0EThus.mp4 270 Laws of exponents https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/x6b17ba59:powers-with-rational-bases/e/exponents_1.5 2023-08-15T19:39:37.8354858Z Exponents with integer bases Practice raising positive and negative numbers (integers only) to whole number powers. Watch out for mischievous negative signs that aren't really part of the base! exercise 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 Laws of exponents