# Surds and Indices Quiz Set 006

### Question 1

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 2

If \$7^{m + n} = 117649\$, and \$7^{m - n} = 49\$, then what is m?

A

4.

B

4.5.

C

5.5.

D

6.5.

Soln.
Ans: a

By inspection, both the expressions can be simplified to \$7^{m + n} = 7^6\$ and \$7^{m - n} = 7^2\$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations \$m + n = 6\$ and \$m - n = 2\$. Solving, we get \$m = {6 + 2}/2\$ = 4. Note: The trick in such type of questions is to keep an eye on the "bases".

### Question 3

If \$2^3.4 = p, and 2^2.6 = q\$ and \$p^m = q^3\$ then what is the value of m?

A

2.29.

B

2.53.

C

2.43.

D

2.83.

Soln.
Ans: a

Substituting in \$p^m = q^3\$, we get \$2^{3.4m} = 2^{2.6 × 3}\$. Bases are same so powers should be same. Hence, \$3.4m = {2.6 × 3}\$, which gives m = 2.29.

### Question 4

If \$√7744 = 88\$, then what is the value of \$√77.44\$ + \$√0.7744\$ + \$√0.007744\$ + \$√0.00007744\$?

A

9.7768.

B

10.2768.

C

11.2768.

D

10.7768.

Soln.
Ans: a

We can see that \$√77.44\$ = 8.8, \$√0.7744\$ = 0.88, \$√0.007744\$ = 0.088, \$√0.00007744\$ = 0.0088. Adding, we get 9.7768 as the answer.

### Question 5

If \$2^x = 16\$, then what is the value of \$2^{x - 1}\$?

A

8.

B

9.

C

7.

D

10.

Soln.
Ans: a

We can write the given expression as \$2^x = 2^4\$. The bases are same so powers should be same. Comparing we get x = 4. So x - 1 = 3, we get \$2^3 = 8\$. 