# Surds and Indices Quiz Set 010

### Question 1

What is \$24^0.06 × 24^x = 24^2.3\$?

A

2.24.

B

2.74.

C

3.74.

D

4.24.

Soln.
Ans: a

We can simplify the given expression to \$24^{0.06 + x} = 24^2.3\$. The bases are equal, so the powers should also be equal. Hence \$0.06 + x = 2.3\$ which gives x = 2.24.

### Question 2

What is \$({7/3})^{x - 2.8} × ({7/3})^x = ({7/3})^0.12\$?

A

1.46.

B

1.96.

C

2.96.

D

3.46.

Soln.
Ans: a

We can simplify the given expression to \$({7/3})^{2x - 2.8} = ({7/3})^0.12\$. The bases are equal, so the powers should also be equal. Hence \$2x - 2.8 = 0.12\$ which gives x = 1.46.

### Question 3

What is \$29^0.8 × 29^x = 29^1.4\$?

A

0.6.

B

1.1.

C

2.1.

D

2.6.

Soln.
Ans: a

We can simplify the given expression to \$29^{0.8 + x} = 29^1.4\$. The bases are equal, so the powers should also be equal. Hence \$0.8 + x = 1.4\$ which gives x = 0.6.

### Question 4

If \$√47\$ is approximately \$6\$, then what is \$47^2\$?

A

1296.

B

1297.

C

1295.

D

1298.

Soln.
Ans: a

Since \$√x = x^{1/2}\$, we can see that \$47^2\$ is same as \$(√47)^4\$ which gives \$6^4\$ = 1296.

### Question 5

What is \$14^1.2 × 14^x = 14^1.4\$?

A

0.2.

B

0.7.

C

1.7.

D

2.2.

Soln.
Ans: a

We can simplify the given expression to \$14^{1.2 + x} = 14^1.4\$. The bases are equal, so the powers should also be equal. Hence \$1.2 + x = 1.4\$ which gives x = 0.2. 