# Surds and Indices Quiz Set 003

### Question 1

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 2

What is \$({11/26})^0.03 × ({11/26})^x = ({11/26})^0.14\$?

A

0.11.

B

0.61.

C

1.61.

D

2.11.

Soln.
Ans: a

We can simplify the given expression to \$({11/26})^{0.03 + x} = ({11/26})^0.14\$. The bases are equal, so the powers should also be equal. Hence \$0.03 + x = 0.14\$ which gives x = 0.11.

### Question 3

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.

### Question 4

What is \$({2/9})^{x - 0.05} × ({2/9})^x = ({2/9})^2.3\$?

A

1.175.

B

1.675.

C

2.675.

D

3.175.

Soln.
Ans: a

We can simplify the given expression to \$({2/9})^{2x - 0.05} = ({2/9})^2.3\$. The bases are equal, so the powers should also be equal. Hence \$2x - 0.05 = 2.3\$ which gives x = 1.175.

### Question 5

If \$p^q = 5\$, then what could be \$(p - 1)^(q + 1)\$?

A

16.

B

17.

C

15.

D

18.

Soln.
Ans: a

By inspection we can see that p = 5, q= 1. So \$(5 - 1)^(1 + 1)\$ will be \$4^2\$, i.e., 16.