https://www.khanacademy.org/math/ka-math-class-7/x26f4f4b84655c15c:exponents-and-powers-ncert-new/x26f4f4b84655c15c:exponents/v/exponents-warmup 2021-07-02T09:35:34Z Exponentiation warmup introduction to exponents and exponential growth Sal Khan video https://cdn.kastatic.org/googleusercontent/pfyzTln_LgIaRts90V4cEWxfSuL9QEN-xonR4S8A9-cNweOXEOOxBppIwIxpmd6ufZQMbHokzX8-cH4Y68VZzLEn Exponentiation warmup introduction to exponents and exponential growth https://cdn.kastatic.org/ka-youtube-converted/UCCNoXqCGZQ.mp4/UCCNoXqCGZQ.mp4 325 Theory of Indices 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 Theory of Indices https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-exponents-and-order-of-operations/cc-6th-exponents/e/positive_and_zero_exponents 2026-04-08T00:54:09.631945657Z Meaning of exponents Practice writing expressions to show what exponents represent. exercise https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-exponents-and-order-of-operations/x0267d782:powers-of-whole-numbers/e/exponents 2025-02-10T05:04:39.155459793Z Powers of whole numbers ​Practice taking positive whole-number exponents of non-negative whole numbers. Lindsay exercise 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 Theory of Indices 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/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 Theory of Indices 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/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 Theory of Indices 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/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-pos-neg-exponents/v/negative-exponent-intuition 2023-07-28T22:13:00.844712665Z 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. Sal Khan video https://cdn.kastatic.org/googleusercontent/TKTmyxQNSjEmHuP-en7bjMh-Q806OYUuV5-VFD_PQ1b8eSkXAGWQdmKHNNCPS23YtCseiKUChkucFhv7rZlI1Sxebg 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/Tqpcku0hrPU.mp4/Tqpcku0hrPU.mp4 278 Theory of Indices 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 Theory of Indices 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/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:rational-exp/v/basic-fractional-exponents 2021-06-30T17:32:34Z Intro to rational exponents What does it mean to take a number by a power which is a unit fraction? For example, what is the result of 3 raised to ½? Sal Khan video https://cdn.kastatic.org/googleusercontent/u1cMPoLA96VGGE3MKU_mWeqxgaGBivp-JTmMQNuqBzESWMHVn0o0nDNA4v8O2qRHpAFbdLwiwCk-pZaBYFlI53zC Intro to rational exponents What does it mean to take a number by a power which is a unit fraction? For example, what is the result of 3 raised to ½? https://cdn.kastatic.org/ka-youtube-converted/lZfXc4nHooo.mp4/lZfXc4nHooo.mp4 300 Theory of Indices https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:rational-exp/e/manipulating-fractional-exponents 2021-07-19T21:05:46.382456182Z Rational exponents challenge Choose equivalent forms of radical and exponential expressions. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:eval-exp-rad/v/fractional-exponents-with-numerators-other-than-1 2021-06-30T17:32:34Z Evaluating fractional exponents Sal shows how to evaluate 64^(2/3) and (8/27)^(-2/3). Sal Khan video https://cdn.kastatic.org/googleusercontent/pXAmfMZsqH2xAtjK2EzBECFVFOnNV4BtHT_nrzCYQeQHRzektnSy0thWzpaUQFhOPH0YoCIx5vlmDpzaw1kBlUKG Evaluating fractional exponents Sal shows how to evaluate 64^(2/3) and (8/27)^(-2/3). https://cdn.kastatic.org/ka-youtube-converted/S34NM0Po0eA.mp4/S34NM0Po0eA.mp4 354 Theory of Indices https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:rational-exp/e/exponents_3 2025-01-22T07:22:50.02175738Z Fractional exponents Evaluate numerical expressions with rational exponents, and convert between equivalent forms of exponential and radical expressions. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:eval-exp-rad/e/simplify-radicals-and-exponentials 2025-01-22T07:22:50.02175738Z Evaluate radical expressions challenge Evaluate numerical radical expressions using the properties of exponents. Tomer Gal exercise