# Surds and Indices Quiz Set 004

### Question 1

If \$34^0.21 = p, and 34^0.22 = q\$ and \$p^m = q^4\$ then what is the value of m?

A

4.19.

B

4.43.

C

4.33.

D

4.73.

Soln.
Ans: a

Substituting in \$p^m = q^4\$, we get \$34^{0.21m} = 34^{0.22 × 4}\$. Bases are same so powers should be same. Hence, \$0.21m = {0.22 × 4}\$, which gives m = 4.19.

### 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

What is the value of x if \$(15625)^1.5 × 5^5\$ ÷ \$625^4.5\$ = \$5^x\$?

A

-4.

B

2.

C

8.

D

14.

Soln.
Ans: a

Simplifying, we get \$(5^6)^1.5 × 5^5\$ ÷ \$(5 ^ 4)^4.5\$ = \$5^x\$, which simplifies to \$5^9 × 5^5\$ ÷ \$5^18\$ = \$5^x.\$ Equating the powers x = 9 + 5 - 18 = -4.

### Question 4

If \$6^x = 7776\$, then what is the value of \$6^{x - 3}\$?

A

36.

B

37.

C

35.

D

38.

Soln.
Ans: a

We can write the given expression as \$6^x = 6^5\$. The bases are same so powers should be same. Comparing we get x = 5. So x - 3 = 2, we get \$6^2 = 36\$.

### Question 5

If \$√73\$ is approximately \$8\$, then what is \$73^3\$?

A

262144.

B

262145.

C

262143.

D

262146.

Soln.
Ans: a

Since \$√x = x^{1/2}\$, we can see that \$73^3\$ is same as \$(√73)^6\$ which gives \$8^6\$ = 262144.