# Surds and Indices Quiz Set 012

### Question 1

If \$4^{m + n} = 4096\$, and \$4^{m - n} = 64\$, then what is m?

A

4.5.

B

5.0.

C

6.0.

D

7.0.

Soln.
Ans: a

By inspection, both the expressions can be simplified to \$4^{m + n} = 4^6\$ and \$4^{m - n} = 4^3\$. 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 = 3\$. Solving, we get \$m = {6 + 3}/2\$ = 4.5. Note: The trick in such type of questions is to keep an eye on the "bases".

### Question 2

What is \$81^0.11 × 81^0.14\$?

A

3.

B

4.

C

2.

D

5.

Soln.
Ans: a

By inspection, we get \$(3^4)^0.11 × (3^4)^0.14\$, which equals \$(3^4)^(0.11 + 0.14)\$, 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 3

What is \$({33/18})^0.18 × ({33/18})^x = ({33/18})^0.3\$?

A

0.12.

B

0.62.

C

1.62.

D

2.12.

Soln.
Ans: a

We can simplify the given expression to \$({33/18})^{0.18 + x} = ({33/18})^0.3\$. The bases are equal, so the powers should also be equal. Hence \$0.18 + x = 0.3\$ which gives x = 0.12.

### Question 4

What is x if \$8^x = 512\$?

A

3.

B

4.

C

2.

D

5.

Soln.
Ans: a

We can write the given expression as \$8^x = 8^3\$. The bases are same so powers should be same. Comparing we get x = 3.

### Question 5

What is \${7^499}/{7^496}\$?

A

343.

B

344.

C

342.

D

345.

Soln.
Ans: a

Simplifying, we get \$7^{499 - 496}\$ which equals\$7^3\$, or 343. This Blog Post/Article "Surds and Indices Quiz Set 012" 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