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:

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

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• 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,
  $$\begin{aligned} \left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^x \\ \text{then, } \frac{ \left( 5^2 \right)^{7.5} \times \left(5 \right)^{2.5} }{\left(5^3 \right)^{1.5} } = 5^x \\ => \text{then, } \frac{ \left( 5^{15} \right) \times \left(5^{2.5} \right) }{\left(5^{4.5} \right) } = 5^x \\ => 5^x = 5^{15 + 2.5 - 4.5} \\ => 5^x = 5^{13} \\ \text{Hence, } x = 13 \end{aligned}$$

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