# Surds and Indices Quiz Set 013

### Question 1

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".

### Question 2

If \$4^0.16 = p, and 4^0.34 = q\$ and \$p^m = q^4\$ then what is the value of m?

A

8.50.

B

8.74.

C

8.64.

D

9.04.

Soln.
Ans: a

Substituting in \$p^m = q^4\$, we get \$4^{0.16m} = 4^{0.34 × 4}\$. Bases are same so powers should be same. Hence, \$0.16m = {0.34 × 4}\$, which gives m = 8.50.

### Question 3

If \$√65\$ is approximately \$8\$, then what is \$65^3.5\$?

A

2097152.

B

2097153.

C

2097151.

D

2097154.

Soln.
Ans: a

Since \$√x = x^{1/2}\$, we can see that \$65^3.5\$ is same as \$(√65)^7\$ which gives \$8^7\$ = 2097152.

### Question 4

What is the value of x if \$(117649)^3.5 × 7^8\$ ÷ \$49^2.5\$ = \$7^x\$?

A

24.

B

30.

C

36.

D

42.

Soln.
Ans: a

Simplifying, we get \$(7^6)^3.5 × 7^8\$ ÷ \$(7 ^ 2)^2.5\$ = \$7^x\$, which simplifies to \$7^21 × 7^8\$ ÷ \$7^5\$ = \$7^x.\$ Equating the powers x = 21 + 8 - 5 = 24.

### Question 5

If \$p^q = 512\$, then what could be \$(p - 1)^(q + 1)\$?

A

2401.

B

2402.

C

2400.

D

2403.

Soln.
Ans: a

By inspection we can see that p = 8, q= 3. So \$(8 - 1)^(3 + 1)\$ will be \$7^4\$, i.e., 2401. 