{"id":246238,"date":"2025-03-24T16:00:56","date_gmt":"2025-03-24T08:00:56","guid":{"rendered":"https:\/\/thepiquelab.com\/blog\/?p=246238"},"modified":"2025-03-25T18:59:30","modified_gmt":"2025-03-25T10:59:30","slug":"exponentials-3-steps-to-simplifying-exponentials-without-calculator","status":"publish","type":"post","link":"https:\/\/thepiquelab.com\/blog\/exponentials-3-steps-to-simplifying-exponentials-without-calculator\/","title":{"rendered":"Exponentials: 3 Steps To Simplifying Exponentials Without Calculator"},"content":{"rendered":"

[et_pb_section fb_built=”1″ _builder_version=”4.21.0″ global_colors_info=”{}”][et_pb_row _builder_version=”4.21.0″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.16″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text _builder_version=”4.21.0″ text_font=”||||||||” hover_enabled=”0″ z_index_tablet=”500″ custom_css_main_element=”sub,||sup {||font-size: 75%;||line-height: 0;||position: relative;||vertical-align: baseline;||}||sup {||top: -0.5em;||}||sub {||bottom: -0.25em;||}” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n

Introduction<\/strong><\/p>\n

How do you simplify a Secondary 3 A-Math<\/span><\/a> exponential expression like the one below, without using a calculator?<\/p>\n

\"The<\/p>\n

Some of you might feel overwhelmed by the terms. But don\u2019t worry because I will teach you a step-by-step guide to solving such complex-looking Exponentials questions.<\/p>\n

You can also watch my explainer video<\/a> for free by visiting our YouTube channel<\/a>.<\/p>\n

\"Click<\/a><\/p>\n

<\/p>\n

<\/p>\n

 <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n\n

Let’s Take A Look At This Exponentials Question<\/span><\/h2>\n

<\/p>\n

<\/p>\n

\"The<\/p>\n

Source: St. Gabriel\u2019s Secondary School \u2013 2020 S3 A-Math SA2 Examination Paper [Q4]<\/span><\/em>
<\/p>\n

\n

Read Also:<\/h3>\n
    \n
  1. [Secondary 3 A-Math Explainer Video] Exponentials : Simplifying Exponentials<\/b><\/a><\/li>\n
  2. Direct Proportion: Finding The Relationship Between Variables\u00a0<\/strong><\/a><\/li>\n<\/ol>\n<\/div>\n

    Step 1\ufe0f\u20e3<\/span>\u00a0Study the terms involved in the expression<\/span><\/h2>\n

    Let us begin by studying the terms involved in this expression.<\/p>\n

    In the term highlighted in yellow below, we notice a base term of 5.<\/p>\n

    \"How<\/p>\n

    Can this term be rewritten to a simpler base?<\/p>\n

    No, it can\u2019t.<\/p>\n

    What about the remaining terms we highlighted in green, blue and orange below? Can they be rewritten to a simpler base?<\/p>\n

    \"How<\/p>\n

    To answer that<\/span>, we will consider the first few powers of 5:<\/p>\n

    <\/p>\n

    \"How<\/p>\n

    What do you notice about the first few powers of 5 and the given terms in our expression? The terms can be rewritten to a common base of 5, which leads us to our next step.<\/p>\n

    Step <\/span>2\ufe0f\u20e3<\/span>\u00a0Rewrite terms to their common bases<\/span><\/h2>\n

    Now, let\u2019s try it out. <\/p>\n

    \"How<\/p>\n

     <\/p>\n

    We can rewrite the term highlighted in green<\/span> as\"\".<\/p>\n

    \"How<\/p>\n

     <\/p>\n

    Let us now move on to the term highlighted in blue.<\/p>\n

    We will have \"\".<\/p>\n

    \"How<\/p>\n

    What about the term highlighted in orange?<\/p>\n

    We will get \"\".<\/p>\n

    \"How<\/strong><\/p>\n

    Now that we have rewritten the terms to their common bases, notice that the green, blue, and orange stripes all contain brackets, which I highlighted in yellow. <\/p>\n

    \"How<\/p>\n

    We can remove these brackets by proceeding with our next step.<\/p>\n

    Step 3\ufe0f\u20e3<\/span>\u00a0Activate the Laws of Indices<\/span><\/h2>\n

    I have discussed the Laws of Indices in detail in a previous blog post. Click this link<\/a> if you want a quick recap of the Laws of Indices.<\/p>\n

    The Law of Indices that we will be using here is as follows:<\/p>\n

    \"How<\/p>\n

    Recall that this law tells us that when we have a base term that has been raised to two powers, first by x<\/em> and then by y<\/em>, we will simplify by multiplying the powers together.<\/p>\n

    Let us try this law in our expression.<\/p>\n

    For the green stripe, when we multiply the powers together, please be careful here and remember that we will distribute the 3 to x<\/em> and 2.<\/p>\n

    \"How<\/p>\n

    Let us move on to the denominator.<\/p>\n

    For the blue stripe, we will get \"\".<\/p>\n

    \"How<\/p>\n

    What about the orange stripe?<\/p>\n

    We will get \"\".<\/p>\n

    \"How<\/p>\n

    Now let us continue by studying our numerator and denominator separately. In the numerator, we see that there is a product of two terms and they share a common base of 5.<\/p>\n

    \"How<\/p>\n

    For expressions in such format, we can simplify them using the following law of indices:<\/p>\n

    \"How<\/p>\n

    Recall that in this law, when we take the product of two terms that share the same base, we simplify them by adding up their powers together.<\/p>\n

    So for the numerator term, we can simplify it by adding up the powers together to get:
    \"How<\/p>\n

    <\/p>\n

    Next, let us look at the denominator:<\/p>\n

    \"How<\/p>\n

    Do you see a common factor? It is \"\".<\/p>\n

    Hence, we can factorise it out and introduce a bracket.<\/p>\n

    What is left in the bracket? It will be 1-10.<\/p>\n

    \"How<\/p>\n

    <\/p>\n

     <\/p>\n

    At this point, do you notice that the numerator and the denominator contain a common-looking term?<\/p>\n

    That term is 54x<\/em><\/sup>.<\/p>\n

    This means that we can simplify further by cancelling the common term highlighted below.<\/p>\n

    But how do we do it?<\/p>\n

    \"How<\/p>\n

    Let us look back at our law of indices and move from right to left.<\/p>\n

    \"How<\/p>\n

    <\/p>\n

    The idea here is to perform a split of the expression into two different parts.<\/p>\n

    \"How<\/p>\n

    Let us look at the numerator. If we split the term according to the law above, we will obtain:<\/p>\n

    \"How<\/p>\n

    In the denominator, we will be left with:<\/p>\n

    \"How<\/p>\n

    We can now cancel the common factor and obtain our final answer. Since we know that 53<\/sup>\u00a0is 125, our final answer will be -125\/9.<\/p>\n

    \"How<\/p>\n

    <\/p>\n

    Suggested Answer<\/span><\/h2>\n

    \"How<\/p>\n

     <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/h2>\n

    Conclusion<\/span><\/h2>\n

    I hope this Exponentials blog post has helped you feel more confident in tackling Exponentials questions, even without using a calculator.<\/p>\n

    To simplify exponentials quickly and accurately, make sure to follow the steps that we discussed:<\/p>\n

    \n

    Step 1\ufe0f\u20e3<\/strong>\u00a0Study the terms involved in the expression<\/p>\n

    Step<\/strong> 2\ufe0f\u20e3\u00a0Rewrite terms to their common bases<\/p>\n

    Step<\/strong> 3\ufe0f\u20e3\u00a0Activate the Laws of Indices<\/p>\n<\/blockquote>\n

    Keep on following our blog posts for more Secondary 3 A-Math<\/a> tips! <\/p>\n

    <\/p>\n

     <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

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    In this article, we’ll be discussing how to solve this Secondary 3 A-Math Exponentials question from St. Gabriel’s Secondary School.<\/p>\n","protected":false},"author":41,"featured_media":246282,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","om_disable_all_campaigns":false,"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"categories":[66,67],"tags":[],"post_folder":[],"modified_by":"Jaimie Aberia","_links":{"self":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/246238"}],"collection":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/users\/41"}],"replies":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/comments?post=246238"}],"version-history":[{"count":9,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/246238\/revisions"}],"predecessor-version":[{"id":246362,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/246238\/revisions\/246362"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media\/246282"}],"wp:attachment":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media?parent=246238"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/categories?post=246238"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/tags?post=246238"},{"taxonomy":"post_folder","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/post_folder?post=246238"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}