Surds and Indices Quiz Set 009

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Question 1

If $7^x = 16807$, then what is the value of $7^{x - 3}$?

 A

49.

 B

50.

 C

48.

 D

51.

Soln.
Ans: a

We can write the given expression as $7^x = 7^5$. The bases are same so powers should be same. Comparing we get x = 5. So x - 3 = 2, we get $7^2 = 49$.


Question 2

If $6^x = 7776$, then what is the value of $6^{x - 3}$?

 A

36.

 B

37.

 C

35.

 D

38.

Soln.
Ans: a

We can write the given expression as $6^x = 6^5$. The bases are same so powers should be same. Comparing we get x = 5. So x - 3 = 2, we get $6^2 = 36$.


Question 3

What is $81^0.19 × 81^0.06$?

 A

3.

 B

4.

 C

2.

 D

5.

Soln.
Ans: a

By inspection, we get $(3^4)^0.19 × (3^4)^0.06$, which equals $(3^4)^(0.19 + 0.06)$, which equals $(3^4)^0.25$, which equals $3^1$, or 3. Note: The trick in such type of questions is to keep an eye on the "bases".


Question 4

If $6^x = 46656$, then what is the value of $6^{x - 1}$?

 A

7776.

 B

7777.

 C

7775.

 D

7778.

Soln.
Ans: a

We can write the given expression as $6^x = 6^6$. The bases are same so powers should be same. Comparing we get x = 6. So x - 1 = 5, we get $6^5 = 7776$.


Question 5

What is ${5^328}/{5^323}$?

 A

3125.

 B

3126.

 C

3124.

 D

3127.

Soln.
Ans: a

Simplifying, we get $5^{328 - 323}$ which equals$5^5$, or 3125.


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This Blog Post/Article "Surds and Indices Quiz Set 009" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-06-24.

Posted by Parveen(Hoven),
Aptitude Trainer


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