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 Indices (advance) https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-pos-neg-exponents/a/negative-exponents-review 2021-06-21T15:29:04Z Negative exponents review Review the basics of negative exponents and try some practice problems.  article 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/rewriting-roots-as-rational-exponents 2022-10-06T23:23:50.639907812Z Rewriting roots as rational exponents Sal solves several problems about the equivalence of expressions with roots and rational exponents. For example, rewrite ⁶√(g⁵) as g^⅚. video https://cdn.kastatic.org/ka_thumbnails_cache/b128fb12-ed74-45d3-b989-7839975723d8_1280_720_base.png Rewriting roots as rational exponents Sal solves several problems about the equivalence of expressions with roots and rational exponents. For example, rewrite ⁶√(g⁵) as g^⅚. https://cdn.kastatic.org/ka-youtube-converted/gH4IsIEYof0.mp4/gH4IsIEYof0.mp4 259 Indices (advance) 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 Indices (advance) https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:eval-exp-rad/v/negative-fractional-exponent-examples 2021-06-30T17:32:35Z Evaluating fractional exponents: negative unit-fraction How to evaluate powers that are negative unit fractions, like 9 raised to -½ and 27 raised to -⅓. Sal Khan video https://cdn.kastatic.org/googleusercontent/5kXZKhHi3eu7P37qoJtnOmz9i_1cqjbvQ3Dc0SIk-1_0Mz0RFNhQpe1LmwG5zRGqMnyqOdLZHsdO1TILloV6kDqU Evaluating fractional exponents: negative unit-fraction How to evaluate powers that are negative unit fractions, like 9 raised to -½ and 27 raised to -⅓. https://cdn.kastatic.org/ka-youtube-converted/tn53EdOr6Rw.mp4/tn53EdOr6Rw.mp4 182 Indices (advance) https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:eval-exp-rad/v/negative-fractional-exponent-examples-2 2021-06-30T17:32:38Z Evaluating fractional exponents: fractional base Sal shows how to evaluate (25/9)^(1/2) and (81/256)^(-1/4). Sal Khan video https://cdn.kastatic.org/googleusercontent/m8wXdCVj032b4chV6iVKkeVptXZOka8Q3FB3lqZjNk1M8lJvXTH-6eEeZM-pBI1AFU0Oo0jeIUwIuIJvxaZ4asTprg Evaluating fractional exponents: fractional base Sal shows how to evaluate (25/9)^(1/2) and (81/256)^(-1/4). https://cdn.kastatic.org/ka-youtube-converted/bIFdW0NZ9W4.mp4/bIFdW0NZ9W4.mp4 204 Indices (advance) https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:eval-exp-rad/v/simplifying-numerical-expression-with-rational-exponents 2022-10-06T23:23:50.639907812Z Evaluating quotient of fractional exponents Sal simplifies the complicated expression 256^(4/7) / 2^(4/7)  until he finds that the expression is equal to 16. video https://cdn.kastatic.org/ka_thumbnails_cache/98e9eadf-308a-456b-afbc-dbe317b37475_1280_720_base.png Evaluating quotient of fractional exponents Sal simplifies the complicated expression 256^(4/7) / 2^(4/7)  until he finds that the expression is equal to 16. https://cdn.kastatic.org/ka-youtube-converted/KGSvigZQKZY.mp4/KGSvigZQKZY.mp4 230 Indices (advance) https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:eval-exp-rad/v/simplifying-with-exponent-properties 2021-06-30T17:32:36Z Evaluating mixed radicals and exponents A worked example of calculating an expression that has both a radical and an exponent. In this example, we evaluate 6^(1/2)⋅(⁵√6)³. Sal Khan video https://cdn.kastatic.org/googleusercontent/zfGQZAHy--CtDW4C_Iq_0ZD8ezaJtvUF3w3-d7unkcxpAmXDyZ1Yi02kAI0bIz7VbV3vGNwbJon5_Lk9clXSaWz8kQ Evaluating mixed radicals and exponents A worked example of calculating an expression that has both a radical and an exponent. In this example, we evaluate 6^(1/2)⋅(⁵√6)³. https://cdn.kastatic.org/ka-youtube-converted/Ht-YXje4R2g.mp4/Ht-YXje4R2g.mp4 171 Indices (advance) https://www.khanacademy.org/math/9th-grade-philippines/x22ecd091eddebb21:2nd-quarter/x22ecd091eddebb21:simplifying-expressions/v/sat-math-p3-easier 2021-02-09T21:48:06Z Radicals and rational exponents — Basic example Watch Sal work through a basic Radicals and rational exponents problem. video https://cdn.kastatic.org/googleusercontent/XVVOUC6gDQystZCCa_ATl-KvOcvkcT-EuAx04JYjSaV3CNs-Y33cI_nVQ1wMaZuj4q984VNaLFn4tmrs4HiQPX4fo9wlMlD7Nm5oPnM Radicals and rational exponents — Basic example Watch Sal work through a basic Radicals and rational exponents problem. https://cdn.kastatic.org/ka-youtube-converted/SgZAuxBCE5w.mp4/SgZAuxBCE5w.mp4 153 Indices (advance) https://www.khanacademy.org/math/cambridge-o-level-mathematics-4024/x3f4c73d082a798eb:algebra-and-graphs/x3f4c73d082a798eb:indices-advance/a/v2-sat-lesson-radicals-and-rational-exponents 2024-10-24T20:36:28.284249064Z Radicals and rational exponents | Lesson A guide to radicals and rational exponents on the digital SAT article https://www.khanacademy.org/math/cambridge-o-level-mathematics-4024/x3f4c73d082a798eb:algebra-and-graphs/x3f4c73d082a798eb:indices-advance/e/v2-radicals-and-rational-exponents-1 2023-12-04T17:55:05.230178085Z Radicals and rational exponents: foundations Radicals and rational exponents: foundations Duo Yang exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:exp-eq-prop/v/solving-exponential-equations-with-exponent-properties 2022-10-06T23:23:50.639907812Z Solving exponential equations using exponent properties Sal solves equations like 26^(9x+5) = 1 and 2^(3x+5) = 64^(x-7). video https://cdn.kastatic.org/ka_thumbnails_cache/145c8dfc-072b-4b28-ba53-000f3fb3fe43_1280_720_base.png Solving exponential equations using exponent properties Sal solves equations like 26^(9x+5) = 1 and 2^(3x+5) = 64^(x-7). https://cdn.kastatic.org/ka-youtube-converted/etl9KKf6se0.mp4/etl9KKf6se0.mp4 296 Indices (advance) https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:exp-eq-prop/a/rational-exponents-radicals-faq 2022-11-24T02:28:55.815015347Z Rational exponents and radicals: FAQ Frequently asked questions about rational exponents and radicals article https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:exp-eq-prop/e/solve-exponential-equations-using-properties-of-exponents--basic- 2025-02-27T11:46:16.621461116Z Solve exponential equations using exponent properties Example: Solve 2^(3x+5) = 64^(x-7). Sid Patel 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 Indices (advance) 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