# Surds and Indices Quiz Set 002

### Question 1

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 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

If \$7^{m + n} = 117649\$, and \$7^{m - n} = 49\$, then what is m?

A

4.

B

4.5.

C

5.5.

D

6.5.

Soln.
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 4

What is x if \$3^x = 27\$?

A

3.

B

4.

C

2.

D

5.

Soln.
Ans: a

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

### Question 5

What is \$6561^0.12 × 6561^0.13\$?

A

9.

B

10.

C

8.

D

11.

Soln.
Ans: a

By inspection, we get \$(3^8)^0.12 × (3^8)^0.13\$, which equals \$(3^8)^(0.12 + 0.13)\$, which equals \$(3^8)^0.25\$, which equals \$3^2\$, or 9. Note: The trick in such type of questions is to keep an eye on the "bases".