Surds and Indices Quiz Set 009

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. 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 2019-08-18.