# Surds and Indices Quiz Set 007

### Question 1

What is \$({11/12})^{x - 0.27} × ({11/12})^x = ({11/12})^0.32\$?

A

0.295.

B

0.795.

C

1.795.

D

2.295.

Soln.
Ans: a

We can simplify the given expression to \$({11/12})^{2x - 0.27} = ({11/12})^0.32\$. The bases are equal, so the powers should also be equal. Hence \$2x - 0.27 = 0.32\$ which gives x = 0.295.

### Question 2

If \$8^{m + n} = 2097152\$, and \$8^{m - n} = 4096\$, then what is m?

A

5.5.

B

6.0.

C

7.0.

D

8.0.

Soln.
Ans: a

By inspection, both the expressions can be simplified to \$8^{m + n} = 8^7\$ and \$8^{m - n} = 8^4\$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations \$m + n = 7\$ and \$m - n = 4\$. Solving, we get \$m = {7 + 4}/2\$ = 5.5. Note: The trick in such type of questions is to keep an eye on the "bases".

### Question 3

What is the value of x if \$(64)^3 × 2^3\$ ÷ \$16^1.5\$ = \$2^x\$?

A

15.

B

21.

C

27.

D

33.

Soln.
Ans: a

Simplifying, we get \$(2^6)^3 × 2^3\$ ÷ \$(2 ^ 4)^1.5\$ = \$2^x\$, which simplifies to \$2^18 × 2^3\$ ÷ \$2^6\$ = \$2^x.\$ Equating the powers x = 18 + 3 - 6 = 15.

### Question 4

What is \$({4/34})^{x - 0.18} × ({4/34})^x = ({4/34})^0.23\$?

A

0.205.

B

0.705.

C

1.705.

D

2.205.

Soln.
Ans: a

We can simplify the given expression to \$({4/34})^{2x - 0.18} = ({4/34})^0.23\$. The bases are equal, so the powers should also be equal. Hence \$2x - 0.18 = 0.23\$ which gives x = 0.205.

### Question 5

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.