1.6E: Exercises

Your Guide to Intermediate Algebra · LibreTexts

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    From LibreTexts, under CC BY-NC-SA 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Practice Makes Perfect

    Simplify Exponents

    Simplify the following

    1. \(2^3\)
    2. \(2^4\)
    3. \(5^1\)
    4. \((\frac{1}{4})^{-2}\)
    5. \(4^{-2}\)
    6. \(2^0\)
    7. \(3-2^2\)
    8. \(2-3^2\)
    9. \((1+2)^3\)
    10. \((2-4)^2\)
    11. \((3+1)^{-2}\)
    12. \(9(−4)÷(−2)^2\)
    13. \((−3)^2÷9+(−2)(−7)\)
    14. \(((2^1)((-3)^3)\)
    Answer
    1. 8
    2. 16
    3. 5
    4. 16
    5. \(\frac{1}{16}\)
    6. 1
    7. 1
    8. -7
    9. 27
    10. 4
    11. \(\frac{1}{16}\)
    12. 9
    13. 15
    14. -54
    Simplify Roots

    In the following exercises, simplify.

    1. \(\sqrt{64}\)
    2. \(-\sqrt{81}\)
    3. \(\sqrt{196}\)
    4. \(-\sqrt{1}\)
    5. \(\sqrt{\frac{4}{9}}\)
    6. \(-\sqrt{0.01}\)
    7. \(121^\frac{1}{2}\)
    8. \(9^\frac{1}{2}\)
    9. \(27^\frac{1}{3}\)
    10. \(\sqrt[3]{8}\)
    11. \(\sqrt[5]{32}\)
    Answer
    1. \(8\)
    2. \(-9\)
    3. \(14\)
    4. ((-1\)
    5. \(\frac{2}{3}\)
    6. \(-0.1\)
    7. 11
    8. 3
    9. 3
    10. 2
    11. 2
    Estimate Roots

    In the following exercises, estimate each root by giving the interval of two consecutive whole numbers in which the root lies.

    1. \(\sqrt{8}\)
    2. \(\sqrt{27}\)
    3. \(\sqrt{70}\)
    4. \(\sqrt[3]{12}\)
    5. \(\sqrt[3]{32}\)
    6. \(\sqrt[3]{71}\)
    Answer
    1. \(2<\sqrt{8}<3\)
    2. \(5<\sqrt{27}<6\)
    3. \(8<\sqrt{70}<9\)
    4. \(2<\sqrt[3]{12}<3\)
    5. \(3<\sqrt[3]{32}<4\)
    6. \(4<\sqrt[3]{71}<5\)
    Simplify with Absolute Values

    In the following exercises, simplify using absolute values as necessary.

    1. \(\sqrt{(-2)^2}\)
    2. \(\sqrt[3]{(-3)^3}\)
    3. \(\sqrt[5]{u^{5}}\)
    4. \(\sqrt[8]{v^{8}}\)
    5. \(\sqrt[4]{y^{4}}\)
    6. \(\sqrt[7]{m^{7}}\)
    7. \(\sqrt{x^{6}}\)
    8. \(\sqrt{y^{16}}\)
    Answer
    1. 2
    2. -3
    3. \(u\)
    4. \(|v|\)
    5. \(|y|\)
    6. \(m\)
    7. \(|x^{3}|\)
    8. \(y^{8}\)

    This page titled 1.6E: Exercises was last modified on Mon, 13 Feb 2023 18:23:53 GMT and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Stanislav A. Trunov and Elizabeth J. Hale via source content that was edited to the style and standards of the LibreTexts platform.