{"id":184,"date":"2022-04-12T09:48:35","date_gmt":"2022-04-12T09:48:35","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=184"},"modified":"2025-02-10T09:24:27","modified_gmt":"2025-02-10T09:24:27","slug":"i-4-exponents-with-negative-bases","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/i-4-exponents-with-negative-bases\/","title":{"rendered":"I.4 Exponents with negative bases"},"content":{"rendered":"\n

Exponents with negative bases<\/strong><\/h2>\n\n\n\n

Key notes:<\/p>\n\n\n\n

Understanding Negative Bases<\/strong>: <\/p>\n\n\n\n

Explain that a negative base in an exponent expression means the base itself is negative, like (-2)^3.<\/p>\n\n\n\n

Odd and Even Powers<\/strong>: <\/p>\n\n\n\n

Discuss how negative bases behave differently with odd and even exponents. For example, (-2)^3 = -8 (odd exponent gives a negative result), but (-2)^2 = 4 (even exponent gives a positive result).<\/p>\n\n\n\n

Calculating Values<\/strong>: <\/p>\n\n\n\n

Show how to calculate expressions like (-3)^2 or (-4)^3 step by step, emphasizing the importance of parentheses to avoid mistakes.<\/p>\n\n\n\n

Rules of Exponents<\/strong>: <\/p>\n\n\n\n

Introduce basic rules such as (-a)^n = -(a^n) for odd n and (-a)^n = (a^n) for even n, highlighting the sign change based on the exponent’s parity.<\/p>\n\n\n\n

Real-World Examples<\/strong>: <\/p>\n\n\n\n

Provide real-world examples where negative exponents might be encountered, like temperatures below zero or debts.<\/p>\n\n\n\n

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An exponent<\/strong> tells you how many times its base<\/strong> is used as a factor.<\/p>\n\n\n\n

Exponents are used to write repeated multiplication.<\/p>\n\n\n\n

For example, for a base of 3:<\/p>\n\n\n\n

\u201332 <\/sup>= \u2013(3 \u00b7 3) = \u20139<\/p>\n\n\n\n

\u201333<\/sup> = \u2013(3 \u00b7 3 \u00b7 3) = \u201327<\/p>\n\n\n\n

\u201334<\/sup> = \u2013(3 \u00b7 3 \u00b7 3 \u00b7 3) = \u201381<\/p>\n\n\n\n

\u201335<\/sup> = \u2013(3 \u00b7 3 \u00b7 3 \u00b7 3 \u00b7 3) = \u2013243<\/p>\n<\/div><\/div>\n\n\n\n

\n

An exponent<\/strong> tells you how many times its base<\/strong> is used as a factor.<\/p>\n\n\n\n

Exponents are used to write repeated multiplication.<\/p>\n\n\n\n

For example, for a base of 2:<\/p>\n\n\n\n

\u201322<\/sup> = \u2013(2 \u00b7 2) = \u20134<\/p>\n\n\n\n

\u201323<\/sup> = \u2013(2 \u00b7 2 \u00b7 2) = \u20138<\/p>\n\n\n\n

\u201324<\/sup> = \u2013(2 \u00b7 2 \u00b7 2 \u00b7 2) = \u201316<\/p>\n\n\n\n

\u201325<\/sup> = \u2013(2 \u00b7 2 \u00b7 2 \u00b7 2 \u00b7 2) = \u201332<\/p>\n<\/div><\/div>\n\n\n\n

\n

An exponent<\/strong> tells you how many times its base<\/strong> is used as a factor.<\/p>\n\n\n\n

Exponents are used to write repeated multiplication.<\/p>\n\n\n\n

For example, for a base of 4:<\/p>\n\n\n\n

\u201342<\/sup> = \u2013(4 \u00b7 4) = \u201316<\/p>\n\n\n\n

\u201343<\/sup> = \u2013(4 \u00b7 4 \u00b7 4) = \u201364<\/p>\n\n\n\n

\u201344<\/sup> = \u2013(4 \u00b7 4 \u00b7 4 \u00b7 4) = \u2013256<\/p>\n\n\n\n

\u201345<\/sup> = \u2013(4 \u00b7 4 \u00b7 4 \u00b7 4 \u00b7 4) = \u20131,024<\/p>\n<\/div><\/div>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

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\n

\ud83d\udce2 Evaluate. – 32<\/sup> = _______<\/strong><\/p>\n<\/div><\/div>\n\n\n\n

The base is 3 (not \u2013<\/sup>3) and the exponent is 2. Use 3 as a factor 2 times. The negative sign stays out in front.<\/p>\n\n\n\n

\u2013 32 <\/sup>= \u2013 (3 \u00b7 3)<\/p>\n\n\n\n

= \u2013 9<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

\ud83d\udce2 Evaluate. – 23<\/sup> = ______<\/strong><\/p>\n<\/div><\/div>\n\n\n\n

The base is 2 (not \u2013<\/sup>2) and the exponent is 3. Use 2 as a factor 3 times. The negative sign stays out in front.<\/p>\n\n\n\n

\u2013 23<\/sup> = \u2013 (2 \u00b7 2 \u00b7 2)<\/p>\n\n\n\n

= \u2013 8<\/p>\n<\/div><\/div>\n\n\n\n

\n

\ud83d\udce2 Evaluate. – 12<\/sup> =<\/strong><\/p>\n\n\n\n

The base is 1 (not \u20131) and the exponent is 2. Use 1 as a factor 2 times. The negative sign stays out in front.<\/p>\n\n\n\n

\u2013 12 = \u2013 (1 \u00b7 1)<\/p>\n\n\n\n

= \u2013 1<\/p>\n<\/div><\/div>\n\n\n\n

let’s practice! \ud83d\udd8a\ufe0f<\/p>\n<\/div><\/div>\n\n\n\n

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Exponents with negative bases Key notes: Understanding Negative Bases: Explain that a negative base in an exponent expression means the base itself is negative, like (-2)^3. Odd and Even Powers: Discuss how negative bases behave differently with odd and even exponents. For example, (-2)^3 = -8 (odd exponent gives a negative result), but (-2)^2 =Continue reading “I.4 Exponents with negative bases”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-184","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/184","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=184"}],"version-history":[{"count":14,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/184\/revisions"}],"predecessor-version":[{"id":15637,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/184\/revisions\/15637"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}