# Surds and Indices Quiz Set 007

### Question 1

If \$3^x = 729\$, then what is the value of \$3^{x - 1}\$?

A

243.

B

244.

C

242.

D

245.

Soln.
Ans: a

We can write the given expression as \$3^x = 3^6\$. The bases are same so powers should be same. Comparing we get x = 6. So x - 1 = 5, we get \$3^5 = 243\$.

### Question 2

What is \$({27/28})^{x - 1.5} × ({27/28})^x = ({27/28})^0.29\$?

A

0.895.

B

1.395.

C

2.395.

D

2.895.

Soln.
Ans: a

We can simplify the given expression to \$({27/28})^{2x - 1.5} = ({27/28})^0.29\$. The bases are equal, so the powers should also be equal. Hence \$2x - 1.5 = 0.29\$ which gives x = 0.895.

### Question 3

What is \$4096^0.15 × 4096^0.1\$?

A

8.

B

9.

C

7.

D

10.

Soln.
Ans: a

By inspection, we get \$(2^12)^0.15 × (2^12)^0.1\$, which equals \$(2^12)^(0.15 + 0.1)\$, which equals \$(2^12)^0.25\$, which equals \$2^3\$, or 8. Note: The trick in such type of questions is to keep an eye on the "bases".

### Question 4

What is \${7^364}/{7^360}\$?

A

2401.

B

2402.

C

2400.

D

2403.

Soln.
Ans: a

Simplifying, we get \$7^{364 - 360}\$ which equals\$7^4\$, or 2401.

### Question 5

What is \$({5/23})^0.05 × ({5/23})^x = ({5/23})^3.2\$?

A

3.15.

B

3.65.

C

4.65.

D

5.15.

Soln.
Ans: a

We can simplify the given expression to \$({5/23})^{0.05 + x} = ({5/23})^3.2\$. The bases are equal, so the powers should also be equal. Hence \$0.05 + x = 3.2\$ which gives x = 3.15. 