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Question 1
What is the value of x if $(15625)^1.5 × 5^5$ ÷ $625^4.5$ = $5^x$?
Question 2
If $7^{m + n} = 117649$, and $7^{m - n} = 49$, then what is m?
4.
4.5.
5.5.
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Ans: a
By inspection, both the expressions can be simplified to $7^{m + n} = 7^6$ and $7^{m - n} = 7^2$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations $m + n = 6$ and $m - n = 2$. Solving, we get $m = {6 + 2}/2$ = 4. Note: The trick in such type of questions is to keep an eye on the "bases".
Question 3
If $2^3.4 = p, and 2^2.6 = q$ and $p^m = q^3$ then what is the value of m?
Question 4
If $√7744 = 88$, then what is the value of $√77.44$ + $√0.7744$ + $√0.007744$ + $√0.00007744$?
Question 5
If $2^x = 16$, then what is the value of $2^{x - 1}$?
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This Blog Post/Article "Surds and Indices Quiz Set 006" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-13