{"id":4764,"date":"2021-11-28T16:28:52","date_gmt":"2021-11-28T16:28:52","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=4764"},"modified":"2022-01-03T07:51:30","modified_gmt":"2022-01-03T07:51:30","slug":"exponential-form-solved-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/exponential-form-solved-examples\/","title":{"rendered":"Exponential form-solved examples"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.13.1″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n

Exponential Form-Solved Examples<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

Exponential form<\/b><\/h2>\n

The exponential form of a number is b^{a}<\/span><\/span>.<\/span><\/p>\n

Here,\u00a0<\/span><\/p>\n

b = base <\/em><\/strong><\/span>= The number which is multiplied with itself multiple times.<\/span><\/p>\n

a = exponent (power)<\/em><\/strong> =<\/span> Number of times the base is multiplied with itself.<\/span><\/p>\n

b^{a}<\/span> <\/span>= exponential form <\/strong><\/em>=<\/span> \u201cb\u201d is multiplied repeatedly \u201ca\u201d times.\u00a0<\/span><\/p>\n

When there are more than 2 unique factors of a number, it is written as the product of two exponential numbers.<\/span><\/p>\n

<\/span><\/p>\n

Examples<\/strong><\/p>\n

1. 8=2 \\times 2 \\times 2=2^{3}<\/span><\/span><\/p>\n

Base = 2<\/span><\/p>\n

Exponent = 3<\/span><\/p>\n

<\/span><\/p>\n

2. 81=3 \\times 3 \\times 3 \\times 3=3^{4}<\/span><\/span><\/p>\n

Base = 3<\/span><\/p>\n

Exponent = 4<\/span><\/p>\n

<\/span><\/p>\n

3. 108=2 \\times 2 \\times 3 \\times 3 \\times 3=2^{2} \\times 3^{3}<\/span><\/span><\/p>\n

 <\/p>\n

The exponent can be a positive integer, negative integer or a fraction.<\/span><\/p>\n

    \n
  1. Positive Exponent (b^{a}<\/span><\/b>)
    <\/b>The positive exponent denotes that the base is multiplied with itself \u201ca\u201d number of times.<\/span>
    <\/span><\/li>\n
  2. Negative Exponent (b^{-a}<\/span><\/b>)
    <\/b>Negative Exponent denotes that the reciprocal of the base is multiplied \u201ca\u201d number of times.<\/span><\/span><\/b><\/b><\/b><\/b><\/b><\/li>\n<\/ol>\n

    3. <\/b>Fractional Exponent <\/b>(b^{\\frac{p}{q}}<\/span><\/b>)<\/b><\/p>\n

    Fractional Exponent denotes powers and roots of the base together.<\/span><\/p>\n

    <\/span><\/p>\n

    b^{\\frac{p}{q}}=\\sqrt[q]{b^{p}}=(\\sqrt[q]{b})^{p}<\/span><\/span><\/p>\n

    Note:<\/strong> b^{\\frac{1}{q}}=q^{t h}<\/span> root of b<\/span><\/p>\n

    <\/span><\/p>\n

    <\/span><\/p>\n

    Solved Examples<\/b><\/h2>\n

    1. Write 3375 in its exponential form.<\/b><\/p>\n

    Solution:<\/strong><\/p>\n

    Prime factorisation of 3375:<\/span><\/p>\n

    \"\"<\/p>\n

    \u21d2 3375 = (3 \u00d7 3 \u00d7 3) \u00d7 (5 \u00d7 5 \u00d7 5)<\/p>\n

    \u21d2 3375=3^{3} \\times 5^{3}=15^{3}<\/span><\/p>\n

     <\/p>\n

    <\/span><\/p>\n

    2. Find the value of 6^{3}<\/span><\/b>.<\/b><\/p>\n

    Solution:<\/strong><\/p>\n

    6^{3}=6 \\times 6 \\times 6=216<\/span><\/span><\/b><\/p>\n

    Hence the value of 6^{3}<\/span> <\/span>is 216.<\/span><\/p>\n

    <\/span><\/p>\n

    <\/b><\/p>\n

    3. Find the value of 5^{-2}<\/span><\/b>.<\/b><\/p>\n

    Solution<\/span><\/p>\n

    Negative Exponent denotes that the reciprocal of the base is multiplied \u201ca\u201d number of times.<\/span><\/p>\n

    b^{-a}=\\frac{1}{b^{a}}<\/span><\/span><\/p>\n

    5^{-2}=\\frac{1}{5^{2}}=\\frac{1}{25}=0.04<\/span><\/span><\/p>\n

    Hence the value of 5^{-2}<\/span>\u00a0<\/span>is equal to 0.04.<\/span><\/p>\n

    <\/span><\/p>\n

    <\/span><\/p>\n

    4. Find the value of 8^{\\frac{2}{3}}<\/span><\/b>.<\/b><\/p>\n

    Solution:<\/strong><\/p>\n

    b^{\\frac{p}{q}}=\\sqrt[q]{b^{p}}=(\\sqrt[q]{b})^{p}<\/span><\/span><\/b><\/p>\n

    8^{\\frac{2}{3}}=(\\sqrt[3]{8})^{2}=2^{2}=4<\/span><\/span><\/b><\/p>\n

    Hence the value of 8^{\\frac{2}{3}}<\/span> <\/span>is equal to 4.<\/span><\/p>\n

      <\/ol>\n

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      Explore Other Topics<\/h1>\n

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      \n
      Geometry<\/a><\/div>\n
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      Related Concepts<\/h1>\n

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      \n
      How to use log table<\/a><\/div>\n
      The value of log 0<\/a><\/a><\/div>\n<\/div>\n

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      [\/et_pb_text][et_pb_image src=”https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/down-circle.png” title_text=”down-circle” show_bottom_space=”off” align=”right” module_class=”img2″ _builder_version=”4.9.10″ _module_preset=”default” width=”44px” height=”18px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”FAQ Row” _builder_version=”4.9.11″ _module_preset=”default” width=”100%” max_width=”1310px” custom_padding=”|40px||40px|false|true” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”FAQ” module_class=”faqstyl” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_font=”|700|||||||” header_text_align=”center” header_line_height=”2.5em” background_color=”#dbedc6″ max_width=”80%” module_alignment=”center” custom_margin=”||||false|false” custom_padding=”30px|25px|30px|25px|true|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”]<\/p>\n

      Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
        <\/ol>\n

        Q1: Define exponential form?<\/strong><\/h3>\n

        Ans: <\/strong><\/span>The exponential form of a number is b^{a}<\/span><\/span>.<\/span><\/p>\n

        Here,\u00a0<\/span><\/p>\n

        b = base <\/span>= The number which is multiplied with itself multiple times.<\/span><\/p>\n

        a = exponent (power) =<\/span> Number of times the base is multiplied with itself.<\/span><\/p>\n

        Q2.<\/strong>What do you mean by negative exponent<\/b>?<\/strong><\/h3>\n

        Ans: <\/strong>Negative Exponent denotes that the reciprocal of the base is multiplied \u201ca\u201d number of times.<\/span><\/p>\n

        b^{-a}=\\frac{1}{b^{a}}<\/span><\/span><\/span><\/p>\n

        3. What do you mean by fractional exponent?<\/b><\/h3>\n

        Ans: <\/b>Fractional Exponent denotes powers and roots of the base together.<\/span><\/p>\n

        b^{\\frac{p}{q}}=\\sqrt[q]{b^{p}}=(\\sqrt[q]{b})^{p}<\/span><\/span><\/p>\n

         <\/p>\n

        [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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