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Surds and Indices Questions Answers

  • 15. \begin{aligned}
    \text{if }6^m = 46656, \\\text{ What is the value of }6^{m-2}
    \end{aligned}

    1. 7776
    2. 7782
    3. 1296
    4. 1290
    Answer And Explanation

    Answer: Option C

    Explanation:

    \begin{aligned}
    6^{m-2}\\ = \dfrac{6^m}{6^2}\\ = \dfrac{46656}{6^2}\\ = \dfrac{46656}{36} = 1296
    \end{aligned}

  • 16. \begin{aligned}
    \left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^?
    \end{aligned}

    1. 9.7
    2. 11.5
    3. 12
    4. 13
    Answer And Explanation

    Answer: Option D

    Explanation:

    Lets assume,
    \begin{aligned}
    \left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^x \\
    \text{then, } \frac{ \left( 5^2 \right)^{7.5} \times \left(5 \right)^{2.5} }{\left(5^3 \right)^{1.5} } = 5^x \\
    => \text{then, } \frac{ \left( 5^{15} \right) \times \left(5^{2.5} \right) }{\left(5^{4.5} \right) } = 5^x \\

    => 5^x = 5^{15 + 2.5 - 4.5} \\
    => 5^x = 5^{13} \\
    \text{Hence, } x = 13
    \end{aligned}